Large Sample Techniques for Statistics

Author: Jiming Jiang
Publisher: Springer Science & Business Media
ISBN: 144196827X
Format: PDF
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In a way, the world is made up of approximations, and surely there is no exception in the world of statistics. In fact, approximations, especially large sample approximations, are very important parts of both theoretical and - plied statistics.TheGaussiandistribution,alsoknownasthe normaldistri- tion,is merelyonesuchexample,dueto thewell-knowncentrallimittheorem. Large-sample techniques provide solutions to many practical problems; they simplify our solutions to di?cult, sometimes intractable problems; they j- tify our solutions; and they guide us to directions of improvements. On the other hand, just because large-sample approximations are used everywhere, and every day, it does not guarantee that they are used properly, and, when the techniques are misused, there may be serious consequences. 2 Example 1 (Asymptotic? distribution). Likelihood ratio test (LRT) is one of the fundamental techniques in statistics. It is well known that, in the 2 “standard” situation, the asymptotic null distribution of the LRT is?,with the degreesoffreedomequaltothe di?erencebetweenthedimensions,de?ned as the numbers of free parameters, of the two nested models being compared (e.g., Rice 1995, pp. 310). This might lead to a wrong impression that the 2 asymptotic (null) distribution of the LRT is always? . A similar mistake 2 might take place when dealing with Pearson’s? -test—the asymptotic distri- 2 2 bution of Pearson’s? -test is not always? (e.g., Moore 1978).

Elements of Large Sample Theory

Author: E.L. Lehmann
Publisher: Springer Science & Business Media
ISBN: 0387227296
Format: PDF, ePub, Mobi
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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.

A Course in Mathematical Statistics and Large Sample Theory

Author: Rabi Bhattacharya
Publisher: Springer
ISBN: 1493940325
Format: PDF, Docs
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This graduate-level textbook is primarily aimed at graduate students of statistics, mathematics, science, and engineering who have had an undergraduate course in statistics, an upper division course in analysis, and some acquaintance with measure theoretic probability. It provides a rigorous presentation of the core of mathematical statistics. Part I of this book constitutes a one-semester course on basic parametric mathematical statistics. Part II deals with the large sample theory of statistics - parametric and nonparametric, and its contents may be covered in one semester as well. Part III provides brief accounts of a number of topics of current interest for practitioners and other disciplines whose work involves statistical methods.

Essential Statistical Inference

Author: Dennis D. Boos
Publisher: Springer Science & Business Media
ISBN: 1461448182
Format: PDF, Mobi
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​This book is for students and researchers who have had a first year graduate level mathematical statistics course. It covers classical likelihood, Bayesian, and permutation inference; an introduction to basic asymptotic distribution theory; and modern topics like M-estimation, the jackknife, and the bootstrap. R code is woven throughout the text, and there are a large number of examples and problems. An important goal has been to make the topics accessible to a wide audience, with little overt reliance on measure theory. A typical semester course consists of Chapters 1-6 (likelihood-based estimation and testing, Bayesian inference, basic asymptotic results) plus selections from M-estimation and related testing and resampling methodology. Dennis Boos and Len Stefanski are professors in the Department of Statistics at North Carolina State. Their research has been eclectic, often with a robustness angle, although Stefanski is also known for research concentrated on measurement error, including a co-authored book on non-linear measurement error models. In recent years the authors have jointly worked on variable selection methods. ​

Theoretical Statistics

Author: Robert W. Keener
Publisher: Springer Science & Business Media
ISBN: 9780387938394
Format: PDF, Mobi
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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.

Testing Statistical Hypotheses

Author: Erich L. Lehmann
Publisher: Springer Science & Business Media
ISBN: 038727605X
Format: PDF, ePub, Mobi
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The third edition of Testing Statistical Hypotheses updates and expands upon the classic graduate text, emphasizing optimality theory for hypothesis testing and confidence sets. The principal additions include a rigorous treatment of large sample optimality, together with the requisite tools. In addition, an introduction to the theory of resampling methods such as the bootstrap is developed. The sections on multiple testing and goodness of fit testing are expanded. The text is suitable for Ph.D. students in statistics and includes over 300 new problems out of a total of more than 760.

Asymptotic Theory of Statistics and Probability

Author: Anirban DasGupta
Publisher: Springer Science & Business Media
ISBN: 0387759700
Format: PDF, Docs
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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.

All of Statistics

Author: Larry Wasserman
Publisher: Springer Science & Business Media
ISBN: 0387217363
Format: PDF, Docs
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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.

Large Sample Methods in Statistics

Author: Pranab K. Sen
Publisher: CRC Press
ISBN: 9780412042218
Format: PDF, ePub, Docs
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This text bridges the gap between sound theoretcial developments and practical, fruitful methodology by providing solid justification for standard symptotic statistical methods. It contains a unified survey of standard large sample theory and provides access to more complex statistical models that arise in diverse practical applications.

Monte Carlo Statistical Methods

Author: Christian Robert
Publisher: Springer Science & Business Media
ISBN: 1475741456
Format: PDF, Kindle
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We have sold 4300 copies worldwide of the first edition (1999). This new edition contains five completely new chapters covering new developments.