Product Description

Approximation Theorems of Mathematical Statistics

This convenient paperback edition makes a seminal text in statistics accessible to a new generation of students and practitioners. Approximation Theorems of Mathematical Statistics covers a broad range of limit theorems useful in mathematical statistics, along with methods of proof and techniques of application. The manipulation of "probability" theorems to obtain "statistical" theorems is emphasized. Besides a knowledge of these basic statistical theorems, this lucid introduction to the subject imparts an appreciation of the instrumental role of probability theory.

The book makes accessible to students and practicing professionals in statistics, general mathematics, operations research, and engineering the essentials of:

• The tools and foundations that are basic to asymptotic theory in statistics
• The asymptotics of statistics computed from a sample, including transformations of vectors of more basic statistics, with emphasis on asymptotic distribution theory and strong convergence
• Important special classes of statistics, such as maximum likelihood estimates and other asymptotic efficient procedures; W. Hoeffding’s U-statistics and R. von Mises’s "differentiable statistical functions"
• Statistics obtained as solutions of equations ("M-estimates"), linear functions of order statistics ("L-statistics"), and rank statistics ("R-statistics")
• Use of influence curves
• Approaches toward asymptotic relative efficiency of statistical test procedures

Product Details

• Amazon Sales Rank: #407975 in Books
• Published on: 2001-12-21
• Original language: English
• Number of items: 1
• Binding: Paperback
• 400 pages

Review
"...even today it still provides a really good introduction into asymptotic statistics..." -- Zentralblatt Math, Vol. 1001, No.01, 2003

From the Publisher
Covers a broad range of limit theorems for mathematical statistics, including proof methods and application techniques. Emphasizes manipulation of probability theorems to obtain statistical theorems. Imparts a knowledge of these basic statistical theorems, as well as an appreciation of the instrumental role of probability theory and a perspective on practical needs for its further development. Assumes introductory graduate knowledge of probability theory and mathematical statistics.

From the Back Cover
Approximation Theorems of Mathematical Statistics

This convenient paperback edition makes a seminal text in statistics accessible to a new generation of students and practitioners. Approximation Theorems of Mathematical Statistics covers a broad range of limit theorems useful in mathematical statistics, along with methods of proof and techniques of application. The manipulation of "probability" theorems to obtain "statistical" theorems is emphasized. Besides a knowledge of these basic statistical theorems, this lucid introduction to the subject imparts an appreciation of the instrumental role of probability theory.

The book makes accessible to students and practicing professionals in statistics, general mathematics, operations research, and engineering the essentials of:

• The tools and foundations that are basic to asymptotic theory in statistics
• The asymptotics of statistics computed from a sample, including transformations of vectors of more basic statistics, with emphasis on asymptotic distribution theory and strong convergence
• Important special classes of statistics, such as maximum likelihood estimates and other asymptotic efficient procedures; W. Hoeffding’s U-statistics and R. von Mises’s "differentiable statistical functions"
• Statistics obtained as solutions of equations ("M-estimates"), linear functions of order statistics ("L-statistics"), and rank statistics ("R-statistics")
• Use of influence curves
• Approaches toward asymptotic relative efficiency of statistical test procedures

Customer Reviews

Great Reference
As a graduate student in statistics, I have had plenty of opportunities to browse through the pages of this book in search of that theorem, technique, or tool that would be applicable to my own work. In many occasions I was succesful in such search. This title compiles and synthesizes a wealth of definitions, theorems, and techniques classically used in asymptotic theory of estimators. It is as much as possible a self-contained work with enough introductory material to be used independently of other references. A bit outdated now, and with minimal material on dependent random variables, this title is still a classic compendium on statistical approximation theory.