Approximation Theorems of Mathematical Statistics

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