Large Sample Techniques for Statistics

Large Sample Techniques for Statistics

Author: Jiming Jiang

Publisher: Springer Science & Business Media

Published: 2010-06-30

Total Pages: 612

ISBN-13: 144196827X

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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

Elements of Large-Sample Theory

Author: E.L. Lehmann

Publisher: Springer Science & Business Media

Published: 2006-04-18

Total Pages: 640

ISBN-13: 0387227296

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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.


Large Sample Methods in Statistics (1994)

Large Sample Methods in Statistics (1994)

Author: Pranab K. Sen

Publisher: CRC Press

Published: 2017-11-22

Total Pages: 381

ISBN-13: 1351361163

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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.


A Course in Large Sample Theory

A Course in Large Sample Theory

Author: Thomas S. Ferguson

Publisher: Routledge

Published: 2017-09-06

Total Pages: 140

ISBN-13: 1351470051

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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.


Large Sample Techniques for Statistics

Large Sample Techniques for Statistics

Author: Jiming Jiang

Publisher: Springer Nature

Published: 2022-04-04

Total Pages: 689

ISBN-13: 3030916952

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This book offers a comprehensive guide to large sample techniques in statistics. With a focus on developing analytical skills and understanding motivation, Large Sample Techniques for Statistics begins with fundamental techniques, and connects theory and applications in engaging ways. The first five chapters review some of the basic techniques, such as the fundamental epsilon-delta arguments, Taylor expansion, different types of convergence, and inequalities. The next five chapters discuss limit theorems in specific situations of observational data. Each of the first ten chapters contains at least one section of case study. The last six chapters are devoted to special areas of applications. This new edition introduces a final chapter dedicated to random matrix theory, as well as expanded treatment of inequalities and mixed effects models. The book's case studies and applications-oriented chapters demonstrate how to use methods developed from large sample theory in real world situations. The book is supplemented by a large number of exercises, giving readers opportunity to practice what they have learned. Appendices provide context for matrix algebra and mathematical statistics. The Second Edition seeks to address new challenges in data science. This text is intended for a wide audience, ranging from senior undergraduate students to researchers with doctorates. A first course in mathematical statistics and a course in calculus are prerequisites..


Frontiers in Massive Data Analysis

Frontiers in Massive Data Analysis

Author: National Research Council

Publisher: National Academies Press

Published: 2013-09-03

Total Pages: 191

ISBN-13: 0309287812

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Data mining of massive data sets is transforming the way we think about crisis response, marketing, entertainment, cybersecurity and national intelligence. Collections of documents, images, videos, and networks are being thought of not merely as bit strings to be stored, indexed, and retrieved, but as potential sources of discovery and knowledge, requiring sophisticated analysis techniques that go far beyond classical indexing and keyword counting, aiming to find relational and semantic interpretations of the phenomena underlying the data. Frontiers in Massive Data Analysis examines the frontier of analyzing massive amounts of data, whether in a static database or streaming through a system. Data at that scale-terabytes and petabytes-is increasingly common in science (e.g., particle physics, remote sensing, genomics), Internet commerce, business analytics, national security, communications, and elsewhere. The tools that work to infer knowledge from data at smaller scales do not necessarily work, or work well, at such massive scale. New tools, skills, and approaches are necessary, and this report identifies many of them, plus promising research directions to explore. Frontiers in Massive Data Analysis discusses pitfalls in trying to infer knowledge from massive data, and it characterizes seven major classes of computation that are common in the analysis of massive data. Overall, this report illustrates the cross-disciplinary knowledge-from computer science, statistics, machine learning, and application disciplines-that must be brought to bear to make useful inferences from massive data.


A Course in Mathematical Statistics and Large Sample Theory

A Course in Mathematical Statistics and Large Sample Theory

Author: Rabi Bhattacharya

Publisher: Springer

Published: 2016-08-13

Total Pages: 386

ISBN-13: 1493940325

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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.


Linear and Generalized Linear Mixed Models and Their Applications

Linear and Generalized Linear Mixed Models and Their Applications

Author: Jiming Jiang

Publisher: Springer Science & Business Media

Published: 2007-05-30

Total Pages: 269

ISBN-13: 0387479465

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This book covers two major classes of mixed effects models, linear mixed models and generalized linear mixed models. It presents an up-to-date account of theory and methods in analysis of these models as well as their applications in various fields. The book offers a systematic approach to inference about non-Gaussian linear mixed models. Furthermore, it includes recently developed methods, such as mixed model diagnostics, mixed model selection, and jackknife method in the context of mixed models. The book is aimed at students, researchers and other practitioners who are interested in using mixed models for statistical data analysis.


Statistical Strategies for Small Sample Research

Statistical Strategies for Small Sample Research

Author: Rick H. Hoyle

Publisher: SAGE Publications

Published: 1999-03-30

Total Pages: 394

ISBN-13: 1506320082

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Newer statistical models, such as structural equation modeling and hierarchical linear modeling, require large sample sizes inappropriate for many research questions or unrealistic for many research arenas. How can researchers get the sophistication and flexibility of large sample studies without the requirement of prohibitively large samples? This book describes and illustrates statistical strategies that meet the sophistication/flexibility criteria for analyzing data from small samples of fewer than 150 cases. Contributions from some of the leading researchers in the field cover the use of multiple imputation software and how it can be used profitably with small data sets and missing data; ways to increase statistical power when sample size cannot be increased; and strategies for computing effect sizes and combining effect sizes across studies. Other contributions describe how to hypothesis test using the bootstrap; methods for pooling effect size indicators from single-case studies; frameworks for drawing inferences from cross-tabulated data; how to determine whether a correlation or covariance matrix warrants structure analysis; and what conditions indicate latent variable modeling is a viable approach to correct for unreliability in the mediator. Other topics include the use of dynamic factor analysis to model temporal processes by analyzing multivariate; time-series data from small numbers of individuals; techniques for coping with estimation problems in confirmatory factor analysis in small samples; how the state space model can be used with surprising accuracy with small data samples; and the use of partial least squares as a viable alternative to covariance-based SEM when the N is small and/or the number of variables in a model is large.