Approximation Theorems of Mathematical Statistics

Approximation Theorems of Mathematical Statistics<br /> <br /> 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.<br /> <br /> The book makes accessible to students and practicing professionals in statistics, general mathematics, operations research, and engineering the essentials of:<br /> * The tools and foundations that are basic to asymptotic theory in statistics<br /> * 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<br /> * 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”<br /> * Statistics obtained as solutions of equations (“M-estimates”), linear functions of order statistics (“L-statistics”), and rank statistics (“R-statistics”)<br /> * Use of influence curves<br /> * Approaches toward asymptotic relative efficiency of statistical test procedures