**Author**: Thomas S. Ferguson

**Publisher:** Chapman & Hall/CRC

**ISBN:** 9781138445765

**Category : **
**Languages : **en

**Pages : **

**Book Description**
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.

**Author**: Thomas S. Ferguson

**Publisher:** Chapman & Hall/CRC

**ISBN:** 9781138445765

**Category : **
**Languages : **en

**Pages : **
**Book Description**
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.

**Author**: Thomas S. Ferguson

**Publisher:** Routledge

**ISBN:** 1351470051

**Category : **Mathematics

**Languages : **en

**Pages : **140

**Book Description**
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.

**Author**: Rabi Bhattacharya

**Publisher:** Springer

**ISBN:** 1493940325

**Category : **Mathematics

**Languages : **en

**Pages : **389

**Book Description**
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.

**Author**: E.L. Lehmann

**Publisher:** Springer Science & Business Media

**ISBN:** 0387227296

**Category : **Mathematics

**Languages : **en

**Pages : **632

**Book Description**
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.

**Author**: Anirban DasGupta

**Publisher:** Springer Science & Business Media

**ISBN:** 0387759700

**Category : **Mathematics

**Languages : **en

**Pages : **726

**Book Description**
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.

**Author**: Pranab K. Sen

**Publisher:** CRC Press

**ISBN:** 9780412042218

**Category : **Mathematics

**Languages : **en

**Pages : **400

**Book Description**
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.

**Author**: Jiming Jiang

**Publisher:** Springer Science & Business Media

**ISBN:** 144196827X

**Category : **Mathematics

**Languages : **en

**Pages : **610

**Book Description**
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).

**Author**: Jiming Jiang

**Publisher:** Springer Nature

**ISBN:** 3030916952

**Category : **Electronic books

**Languages : **en

**Pages : **689

**Book Description**
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.

**Author**: J.G. Kalbfleisch

**Publisher:** Springer

**ISBN:** 9781461251361

**Category : **Mathematics

**Languages : **en

**Pages : **0

**Book Description**
This book is in two volumes, and is intended as a text for introductory courses in probability and statistics at the second or third year university level. It em phasizes applications and logical principles rather than mathematical theory. A good background in freshman calculus is sufficient for most of the material presented. Several starred sections have been included as supplementary material. Nearly 900 problems and exercises of varying difficulty are given, and Appendix A contains answers to about one-third of them. The first volume (Chapters 1-8) deals with probability models and with math ematical methods for describing and manipulating them. It is similar in content and organization to the 1979 edition. Some sections have been rewritten and expanded-for example, the discussions of independent random variables and conditional probability. Many new exercises have been added. In the second volume (Chapters 9-16), probability models are used as the basis for the analysis and interpretation of data. This material has been revised extensively. Chapters 9 and 10 describe the use of the likelihood function in estimation problems, as in the 1979 edition. Chapter 11 then discusses frequency properties of estimation procedures, and introduces coverage probability and confidence intervals. Chapter 12 describes tests of significance, with applications primarily to frequency data. The likelihood ratio statistic is used to unify the material on testing, and connect it with earlier material on estimation.

**Author**: Taylor & Francis Group

**Publisher:**
**ISBN:** 9781138061101

**Category : **
**Languages : **en

**Pages : **
**Book Description**