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| asymptotic statistics van der vaart: Asymptotic Statistics A. W. van der Vaart, 2000-06-19 This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master s level statistics text, this book will also give researchers an overview of the latest research in asymptotic statistics. |
| asymptotic statistics van der vaart: Asymptotic Statistics A. W. van der Vaart, 2000-06-19 This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master s level statistics text, this book will also give researchers an overview of the latest research in asymptotic statistics. |
| asymptotic statistics van der vaart: Asymptotic Statistics A. W. van der Vaart, 2000-06-19 This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master's level statistics text, this book will also give researchers an overview of research in asymptotic statistics. |
| asymptotic statistics van der vaart: Asymptotic Statistics A. W. van der Vaart, 1998 This book is an introduction to the field of asymptotic statistics. The treatment is both practical and mathematically rigorous. In addition to most of the standard topics of an asymptotics course, including likelihood inference, M-estimation, the theory of asymptotic efficiency, U-statistics, and rank procedures, the book also presents recent research topics such as semiparametric models, the bootstrap, and empirical processes and their applications. The topics are organized from the central idea of approximation by limit experiments, which gives the book one of its unifying themes. This entails mainly the local approximation of the classical i.i.d. set up with smooth parameters by location experiments involving a single, normally distributed observation. Thus, even the standard subjects of asymptotic statistics are presented in a novel way. Suitable as a graduate or Master's level statistics text, this book will also give researchers an overview of research in asymptotic statistics. |
| asymptotic statistics van der vaart: Asymptotics in Statistics Lucien Le Cam, Grace Lo Yang, 2012-12-06 This is the second edition of a coherent introduction to the subject of asymptotic statistics as it has developed over the past 50 years. It differs from the first edition in that it is now more 'reader friendly' and also includes a new chapter on Gaussian and Poisson experiments, reflecting their growing role in the field. Most of the subsequent chapters have been entirely rewritten and the nonparametrics of Chapter 7 have been amplified. The volume is not intended to replace monographs on specialized subjects, but will help to place them in a coherent perspective. It thus represents a link between traditional material - such as maximum likelihood, and Wald's Theory of Statistical Decision Functions -- together with comparison and distances for experiments. Much of the material has been taught in a second year graduate course at Berkeley for 30 years. |
| asymptotic statistics van der vaart: Asymptotic Theory of Statistics and Probability Anirban DasGupta, 2008-03-07 This unique book delivers an encyclopedic treatment of classic as well as contemporary large sample theory, dealing with both statistical problems and probabilistic issues and tools. The book is unique in its detailed coverage of fundamental topics. It is written in an extremely lucid style, with an emphasis on the conceptual discussion of the importance of a problem and the impact and relevance of the theorems. There is no other book in large sample theory that matches this book in coverage, exercises and examples, bibliography, and lucid conceptual discussion of issues and theorems. |
| asymptotic statistics van der vaart: Mathematical Statistics Aleksandr Petrovich Korostelev, Olga Korosteleva, 2011 iPositive Give a man a fish, he eats for a day, but if you teach him to fish, you feed him for life. Such is the approach of iPositive. One day at the gym doesnt make a person fit for life; its a consistent dedication to getting the body in shape that eventually yields results. The lessons in iPositive work in much the same way: They challenge the reader to work to keep the mind in shape. The book is a powerful guide to personal happiness through positivity. Its concepts provide empowerment to overcome self-doubt, disbelief and inferiority complexes in order to transcend the negativity in life. iPositive is geared toward helping individuals become more focused on the things they most want in life, like happiness, love and success, or banish anchors that may be weighting them down, like stress, smoking or excess weight. The book gives readers the practical means to become more focused on those things they want in life, and serves as an inspirational manual for a life of fulfillment, and strength in body, mind and spirit. |
| asymptotic statistics van der vaart: Introduction to Empirical Processes and Semiparametric Inference Michael R. Kosorok, 2007-12-29 Kosorok’s brilliant text provides a self-contained introduction to empirical processes and semiparametric inference. These powerful research techniques are surprisingly useful for developing methods of statistical inference for complex models and in understanding the properties of such methods. This is an authoritative text that covers all the bases, and also a friendly and gradual introduction to the area. The book can be used as research reference and textbook. |
| asymptotic statistics van der vaart: Fundamentals of Nonparametric Bayesian Inference Subhashis Ghosal, A. W. van der Vaart, 2017-06-26 Bayesian nonparametrics comes of age with this landmark text synthesizing theory, methodology and computation. |
| asymptotic statistics van der vaart: Higher Order Asymptotics J. K. Ghosh, 1994 |
| asymptotic statistics van der vaart: Asymptotic Methods in Statistical Decision Theory Lucien Le Cam, 2012-12-06 This book grew out of lectures delivered at the University of California, Berkeley, over many years. The subject is a part of asymptotics in statistics, organized around a few central ideas. The presentation proceeds from the general to the particular since this seemed the best way to emphasize the basic concepts. The reader is expected to have been exposed to statistical thinking and methodology, as expounded for instance in the book by H. Cramer [1946] or the more recent text by P. Bickel and K. Doksum [1977]. Another pos sibility, closer to the present in spirit, is Ferguson [1967]. Otherwise the reader is expected to possess some mathematical maturity, but not really a great deal of detailed mathematical knowledge. Very few mathematical objects are used; their assumed properties are simple; the results are almost always immediate consequences of the definitions. Some objects, such as vector lattices, may not have been included in the standard background of a student of statistics. For these we have provided a summary of relevant facts in the Appendix. The basic structures in the whole affair are systems that Blackwell called experiments and transitions between them. An experiment is a mathe matical abstraction intended to describe the basic features of an observational process if that process is contemplated in advance of its implementation. Typically, an experiment consists of a set E> of theories about what may happen in the observational process. |
| asymptotic statistics van der vaart: Statistical Models Based on Counting Processes Per K. Andersen, Ornulf Borgan, Richard D. Gill, Niels Keiding, 2012-12-06 Modern survival analysis and more general event history analysis may be effectively handled within the mathematical framework of counting processes. This book presents this theory, which has been the subject of intense research activity over the past 15 years. The exposition of the theory is integrated with careful presentation of many practical examples, drawn almost exclusively from the authors'own experience, with detailed numerical and graphical illustrations. Although Statistical Models Based on Counting Processes may be viewed as a research monograph for mathematical statisticians and biostatisticians, almost all the methods are given in concrete detail for use in practice by other mathematically oriented researchers studying event histories (demographers, econometricians, epidemiologists, actuarial mathematicians, reliability engineers and biologists). Much of the material has so far only been available in the journal literature (if at all), and so a wide variety of researchers will find this an invaluable survey of the subject. |
| asymptotic statistics van der vaart: A Course in Large Sample Theory Thomas S. Ferguson, 2017-09-06 A Course in Large Sample Theory is presented in four parts. The first treats basic probabilistic notions, the second features the basic statistical tools for expanding the theory, the third contains special topics as applications of the general theory, and the fourth covers more standard statistical topics. Nearly all topics are covered in their multivariate setting.The book is intended as a first year graduate course in large sample theory for statisticians. It has been used by graduate students in statistics, biostatistics, mathematics, and related fields. Throughout the book there are many examples and exercises with solutions. It is an ideal text for self study. |
| asymptotic statistics van der vaart: High-Dimensional Statistics Martin J. Wainwright, 2019-02-21 A coherent introductory text from a groundbreaking researcher, focusing on clarity and motivation to build intuition and understanding. |
| asymptotic statistics van der vaart: A User's Guide to Measure Theoretic Probability David Pollard, 2002 This book grew from a one-semester course offered for many years to a mixed audience of graduate and undergraduate students who have not had the luxury of taking a course in measure theory. The core of the book covers the basic topics of independence, conditioning, martingales, convergence in distribution, and Fourier transforms. In addition there are numerous sections treating topics traditionally thought of as more advanced, such as coupling and the KMT strong approximation, option pricing via the equivalent martingale measure, and the isoperimetric inequality for Gaussian processes. The book is not just a presentation of mathematical theory, but is also a discussion of why that theory takes its current form. It will be a secure starting point for anyone who needs to invoke rigorous probabilistic arguments and understand what they mean. |
| asymptotic statistics van der vaart: All of Statistics Larry Wasserman, 2013-12-11 Taken literally, the title All of Statistics is an exaggeration. But in spirit, the title is apt, as the book does cover a much broader range of topics than a typical introductory book on mathematical statistics. This book is for people who want to learn probability and statistics quickly. It is suitable for graduate or advanced undergraduate students in computer science, mathematics, statistics, and related disciplines. The book includes modern topics like non-parametric curve estimation, bootstrapping, and classification, topics that are usually relegated to follow-up courses. The reader is presumed to know calculus and a little linear algebra. No previous knowledge of probability and statistics is required. Statistics, data mining, and machine learning are all concerned with collecting and analysing data. |
| asymptotic statistics van der vaart: Extremes and Related Properties of Random Sequences and Processes M. R. Leadbetter, G. Lindgren, H. Rootzen, 2012-12-06 Classical Extreme Value Theory-the asymptotic distributional theory for maxima of independent, identically distributed random variables-may be regarded as roughly half a century old, even though its roots reach further back into mathematical antiquity. During this period of time it has found significant application-exemplified best perhaps by the book Statistics of Extremes by E. J. Gumbel-as well as a rather complete theoretical development. More recently, beginning with the work of G. S. Watson, S. M. Berman, R. M. Loynes, and H. Cramer, there has been a developing interest in the extension of the theory to include, first, dependent sequences and then continuous parameter stationary processes. The early activity proceeded in two directions-the extension of general theory to certain dependent sequences (e.g., Watson and Loynes), and the beginning of a detailed theory for stationary sequences (Berman) and continuous parameter processes (Cramer) in the normal case. In recent years both lines of development have been actively pursued. |
| asymptotic statistics van der vaart: A Probability Path Sidney I. Resnick, 2013-11-30 |
| asymptotic statistics van der vaart: Elements of Large-Sample Theory E.L. Lehmann, 2006-04-18 Written by one of the main figures in twentieth century statistics, this book provides a unified treatment of first-order large-sample theory. It discusses a broad range of applications including introductions to density estimation, the bootstrap, and the asymptotics of survey methodology. The book is written at an elementary level making it accessible to most readers. |
| asymptotic statistics van der vaart: Theoretical Statistics Robert W. Keener, 2010-09-08 Intended as the text for a sequence of advanced courses, this book covers major topics in theoretical statistics in a concise and rigorous fashion. The discussion assumes a background in advanced calculus, linear algebra, probability, and some analysis and topology. Measure theory is used, but the notation and basic results needed are presented in an initial chapter on probability, so prior knowledge of these topics is not essential. The presentation is designed to expose students to as many of the central ideas and topics in the discipline as possible, balancing various approaches to inference as well as exact, numerical, and large sample methods. Moving beyond more standard material, the book includes chapters introducing bootstrap methods, nonparametric regression, equivariant estimation, empirical Bayes, and sequential design and analysis. The book has a rich collection of exercises. Several of them illustrate how the theory developed in the book may be used in various applications. Solutions to many of the exercises are included in an appendix. |
| asymptotic statistics van der vaart: Statistical Analysis of Stochastic Processes in Time J. K. Lindsey, 2004-08-02 This book was first published in 2004. Many observed phenomena, from the changing health of a patient to values on the stock market, are characterised by quantities that vary over time: stochastic processes are designed to study them. This book introduces practical methods of applying stochastic processes to an audience knowledgeable only in basic statistics. It covers almost all aspects of the subject and presents the theory in an easily accessible form that is highlighted by application to many examples. These examples arise from dozens of areas, from sociology through medicine to engineering. Complementing these are exercise sets making the book suited for introductory courses in stochastic processes. Software (available from www.cambridge.org) is provided for the freely available R system for the reader to apply to all the models presented. |
| asymptotic statistics van der vaart: Mathematical Statistics Thomas S. Ferguson, 2014-07-10 Mathematical Statistics: A Decision Theoretic Approach presents an investigation of the extent to which problems of mathematical statistics may be treated by decision theory approach. This book deals with statistical theory that could be justified from a decision-theoretic viewpoint. Organized into seven chapters, this book begins with an overview of the elements of decision theory that are similar to those of the theory of games. This text then examines the main theorems of decision theory that involve two more notions, namely the admissibility of a decision rule and the completeness of a class of decision rules. Other chapters consider the development of theorems in decision theory that are valid in general situations. This book discusses as well the invariance principle that involves groups of transformations over the three spaces around which decision theory is built. The final chapter deals with sequential decision problems. This book is a valuable resource for first-year graduate students in mathematics. |
| asymptotic statistics van der vaart: Quantum State Diffusion Ian Percival, 1998-12-10 The first book devoted to quantum state diffusion - suitable for graduate students and researchers. |
| asymptotic statistics van der vaart: Probability in Banach Spaces Michel Ledoux, Michel Talagrand, 2013-03-09 Isoperimetric, measure concentration and random process techniques appear at the basis of the modern understanding of Probability in Banach spaces. Based on these tools, the book presents a complete treatment of the main aspects of Probability in Banach spaces (integrability and limit theorems for vector valued random variables, boundedness and continuity of random processes) and of some of their links to Geometry of Banach spaces (via the type and cotype properties). Its purpose is to present some of the main aspects of this theory, from the foundations to the most important achievements. The main features of the investigation are the systematic use of isoperimetry and concentration of measure and abstract random process techniques (entropy and majorizing measures). Examples of these probabilistic tools and ideas to classical Banach space theory are further developed. |
| asymptotic statistics van der vaart: Introduction to Nonparametric Estimation Alexandre B. Tsybakov, 2008-10-22 Developed from lecture notes and ready to be used for a course on the graduate level, this concise text aims to introduce the fundamental concepts of nonparametric estimation theory while maintaining the exposition suitable for a first approach in the field. |
| asymptotic statistics van der vaart: Mathematical Foundations of Infinite-Dimensional Statistical Models Evarist Giné, Richard Nickl, 2021-03-25 In nonparametric and high-dimensional statistical models, the classical Gauss–Fisher–Le Cam theory of the optimality of maximum likelihood estimators and Bayesian posterior inference does not apply, and new foundations and ideas have been developed in the past several decades. This book gives a coherent account of the statistical theory in infinite-dimensional parameter spaces. The mathematical foundations include self-contained 'mini-courses' on the theory of Gaussian and empirical processes, approximation and wavelet theory, and the basic theory of function spaces. The theory of statistical inference in such models - hypothesis testing, estimation and confidence sets - is presented within the minimax paradigm of decision theory. This includes the basic theory of convolution kernel and projection estimation, but also Bayesian nonparametrics and nonparametric maximum likelihood estimation. In a final chapter the theory of adaptive inference in nonparametric models is developed, including Lepski's method, wavelet thresholding, and adaptive inference for self-similar functions. Winner of the 2017 PROSE Award for Mathematics. |
| asymptotic statistics van der vaart: Approximate Distributions of Order Statistics Rolf-Dieter Reiss, 2012-12-06 This book is designed as a unified and mathematically rigorous treatment of some recent developments of the asymptotic distribution theory of order statistics (including the extreme order statistics) that are relevant for statistical theory and its applications. Particular emphasis is placed on results concern ing the accuracy oflimit theorems, on higher order approximations, and other approximations in quite a general sense. Contrary to the classical limit theorems that primarily concern the weak convergence of distribution functions, our main results will be formulated in terms of the variational and the Hellinger distance. These results will form the proper springboard for the investigation of parametric approximations of nonparametric models of joint distributions of order statistics. The approxi mating models include normal as well as extreme value models. Several applications will show the usefulness of this approach. Other recent developments in statistics like nonparametric curve estima tion and the bootstrap method will be studied as far as order statistics are concerned. 1n connection with this, graphical methods will, to some extent, be explored. |
| asymptotic statistics van der vaart: Empirical Processes in M-Estimation Sara A. Geer, 2000-01-28 Advanced text; estimation methods in statistics, e.g. least squares; lots of examples; minimal abstraction. |
| asymptotic statistics van der vaart: Asymptotic Techniques for Use in Statistics O. E. Barndorff-Nielsen, D. R. Cox, 1989-03 The use in statistical theory of approximate arguments based on such methods as local linearization (the delta method) and approxi mate normality has a long history. Such ideas play at least three roles. First they may give simple approximate answers to distributional problems where an exact solution is known in principle but difficult to implement. The second role is to yield higher-order expansions from which the accuracy of simple approximations may be assessed and where necessary improved. Thirdly the systematic development of a theoretical approach to statistical inference that will apply to quite general families of statistical models demands an asymptotic formulation, as far as possible one that will recover 'exact' results where these are available. The approximate arguments are developed by supposing that some defining quantity, often a sample size but more generally an amount of information, becomes large: it must be stressed that this is a technical device for generating approximations whose adequacy always needs assessing, rather than a 'physical' limiting notion. Of the three roles outlined above, the first two are quite close to the traditional roles of asymptotic expansions in applied mathematics and much ofthe very extensive literature on the asymptotic expansion of integrals and of the special functions of mathematical physics is quite directly relevant, although the recasting of these methods into a probability mould is quite often enlightening. |
| asymptotic statistics van der vaart: An Introduction to Mathematical Statistics Fetsje Bijma, Marianne Jonker, A. W. van der Vaart, 2017 This book gives an introduction into mathematical statistics. |
| asymptotic statistics van der vaart: Nonparametric and Semiparametric Models Wolfgang Karl Härdle, Marlene Müller, Stefan Sperlich, Axel Werwatz, 2012-08-27 The statistical and mathematical principles of smoothing with a focus on applicable techniques are presented in this book. It naturally splits into two parts: The first part is intended for undergraduate students majoring in mathematics, statistics, econometrics or biometrics whereas the second part is intended to be used by master and PhD students or researchers. The material is easy to accomplish since the e-book character of the text gives a maximum of flexibility in learning (and teaching) intensity. |
| asymptotic statistics van der vaart: Statistical Models A. C. Davison, 2008-06-30 Models and likelihood are the backbone of modern statistics and data analysis. The coverage is unrivaled, with sections on survival analysis, missing data, Markov chains, Markov random fields, point processes, graphical models, simulation and Markov chain Monte Carlo, estimating functions, asymptotic approximations, local likelihood and spline regressions as well as on more standard topics. Anthony Davison blends theory and practice to provide an integrated text for advanced undergraduate and graduate students, researchers and practicioners. Its comprehensive coverage makes this the standard text and reference in the subject. |
| asymptotic statistics van der vaart: Measures, Integrals and Martingales René L. Schilling, 2005-11-10 This book, first published in 2005, introduces measure and integration theory as it is needed in many parts of analysis and probability. |
| asymptotic statistics van der vaart: Adventures in Stochastic Processes Sidney I. Resnick, 2013-12-11 Stochastic processes are necessary ingredients for building models of a wide variety of phenomena exhibiting time varying randomness. This text offers easy access to this fundamental topic for many students of applied sciences at many levels. It includes examples, exercises, applications, and computational procedures. It is uniquely useful for beginners and non-beginners in the field. No knowledge of measure theory is presumed. |
| asymptotic statistics van der vaart: Understanding Advanced Statistical Methods Peter Westfall, Kevin S. S. Henning, 2013-04-09 Providing a much-needed bridge between elementary statistics courses and advanced research methods courses, Understanding Advanced Statistical Methods helps students grasp the fundamental assumptions and machinery behind sophisticated statistical topics, such as logistic regression, maximum likelihood, bootstrapping, nonparametrics, and Bayesian methods. The book teaches students how to properly model, think critically, and design their own studies to avoid common errors. It leads them to think differently not only about math and statistics but also about general research and the scientific method. With a focus on statistical models as producers of data, the book enables students to more easily understand the machinery of advanced statistics. It also downplays the population interpretation of statistical models and presents Bayesian methods before frequentist ones. Requiring no prior calculus experience, the text employs a just-in-time approach that introduces mathematical topics, including calculus, where needed. Formulas throughout the text are used to explain why calculus and probability are essential in statistical modeling. The authors also intuitively explain the theory and logic behind real data analysis, incorporating a range of application examples from the social, economic, biological, medical, physical, and engineering sciences. Enabling your students to answer the why behind statistical methods, this text teaches them how to successfully draw conclusions when the premises are flawed. It empowers them to use advanced statistical methods with confidence and develop their own statistical recipes. Ancillary materials are available on the book’s website. |
| asymptotic statistics van der vaart: Design of Comparative Experiments R. A. Bailey, 2008-04-17 This book should be on the shelf of every practising statistician who designs experiments. Good design considers units and treatments first, and then allocates treatments to units. It does not choose from a menu of named designs. This approach requires a notation for units that does not depend on the treatments applied. Most structure on the set of observational units, or on the set of treatments, can be defined by factors. This book develops a coherent framework for thinking about factors and their relationships, including the use of Hasse diagrams. These are used to elucidate structure, calculate degrees of freedom and allocate treatment subspaces to appropriate strata. Based on a one-term course the author has taught since 1989, the book is ideal for advanced undergraduate and beginning graduate courses. Examples, exercises and discussion questions are drawn from a wide range of real applications: from drug development, to agriculture, to manufacturing. |
| asymptotic statistics van der vaart: Festschrift for Lucien Le Cam David Pollard, Erik Torgersen, Grace L. Yang, 2012-12-06 Contributed in honour of Lucien Le Cam on the occasion of his 70th birthday, the papers reflect the immense influence that his work has had on modern statistics. They include discussions of his seminal ideas, historical perspectives, and contributions to current research - spanning two centuries with a new translation of a paper of Daniel Bernoulli. The volume begins with a paper by Aalen, which describes Le Cams role in the founding of the martingale analysis of point processes, and ends with one by Yu, exploring the position of just one of Le Cams ideas in modern semiparametric theory. The other 27 papers touch on areas such as local asymptotic normality, contiguity, efficiency, admissibility, minimaxity, empirical process theory, and biological medical, and meteorological applications - where Le Cams insights have laid the foundations for new theories. |
| asymptotic statistics van der vaart: Student Solution Manual for Essential Mathematical Methods for the Physical Sciences K. F. Riley, M. P. Hobson, 2011-02-17 This Student Solution Manual provides complete solutions to all the odd-numbered problems in Essential Mathematical Methods for the Physical Sciences. It takes students through each problem step-by-step, so they can clearly see how the solution is reached, and understand any mistakes in their own working. Students will learn by example how to select an appropriate method, improving their problem-solving skills. |
| asymptotic statistics van der vaart: Efficient and Adaptive Estimation for Semiparametric Models Peter J. Bickel, Chris A.J. Klaassen, Ya'acov Ritov, Jon A. Wellner, 1998-06-01 This book deals with estimation in situations in which there is believed to be enough information to model parametrically some, but not all of the features of a data set. Such models have arisen in a wide context in recent years, and involve new nonlinear estimation procedures. Statistical models of this type are directly applicable to fields such as economics, epidemiology, and astronomy. |
| asymptotic statistics van der vaart: Measure Theory and Filtering Lakhdar Aggoun, Robert J. Elliott, 2004-09-13 The estimation of noisily observed states from a sequence of data has traditionally incorporated ideas from Hilbert spaces and calculus-based probability theory. As conditional expectation is the key concept, the correct setting for filtering theory is that of a probability space. Graduate engineers, mathematicians and those working in quantitative finance wishing to use filtering techniques will find in the first half of this book an accessible introduction to measure theory, stochastic calculus, and stochastic processes, with particular emphasis on martingales and Brownian motion. Exercises are included. The book then provides an excellent users' guide to filtering: basic theory is followed by a thorough treatment of Kalman filtering, including recent results which extend the Kalman filter to provide parameter estimates. These ideas are then applied to problems arising in finance, genetics and population modelling in three separate chapters, making this a comprehensive resource for both practitioners and researchers. |
Explaining the relevance of asymptotic complexity of algorithms to ...
It is good to compare the asymptotic analysis to other approaches for predicting the performance of algorithms and comparing them. One common approach is performance tests against …
What is the asymptotic runtime of this nested loop? [duplicate]
The result is correct, but your reasoning is not. You can't mix big-oh with ellipses. It happens to work here because of extra conditions that happen to be true but that you haven't checked.
What is an asymptotically tight upper bound?
Dec 20, 2013 · $\begingroup$ +1, but I think a danger in your choice of example is that it can be misinterpreted to be claiming that for an upper bound to be asymptotically tight, it must be that …
Calculator for time complexity of recursive functions
Jan 30, 2021 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for …
Asymptotic analysis for machine learning algorithms
Feb 9, 2020 · Asymptotic Complexity and real life situations are different. Please take a look at this Question. Now, machine learning is a very hard topic to explore precisely the asymptotic …
Big-O complexity of sqrt(n) - Computer Science Stack Exchange
Sep 6, 2016 · I'm trying to backfill missing CS knowledge and going through the MIT 6.006 course. It asks me to rank functions by asymptotic complexity and I want to understand how they …
Operations on asymptotic notations - Computer Science Stack …
You cannot divide asymptotic notations in this way, since big O is only an upper bound. For example, if ...
landau notation - Asymptotic Analysis for two variables?
How is asymptotic analysis (big o, little o, big theta, big theta etc.) defined for functions with multiple variables? I know that the Wikipedia article has a section on it, but it uses a lot of …
asymptotics - Solving or approximating recurrence relations for ...
respectively. Note that the base cases are not stated or used here; that makes sense, considering we are only investigating asymptotic behaviour. We silently assume that they are some …
Solving a recurrence relation with √n as parameter
Given below, there are some good solutions to find the closed form expression, which also give the asymptotic complexity. However, if you only need the asymptotic complexity, the analysis is …
Explaining the relevance of asymptotic complexity of algo…
It is good to compare the asymptotic analysis to other approaches for predicting the performance of …
What is the asymptotic runtime of this nested loop? [duplicate]
The result is correct, but your reasoning is not. You can't mix big-oh with ellipses. It happens to work …
What is an asymptotically tight upper bound?
Dec 20, 2013 · $\begingroup$ +1, but I think a danger in your choice of example is that it can be …
Calculator for time complexity of recursive functions
Jan 30, 2021 · Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack …
Asymptotic analysis for machine learning algorithms
Feb 9, 2020 · Asymptotic Complexity and real life situations are different. Please take a look at this Question. Now, …
