Probability Theory and Extreme Value Theory

01/07 This title is now available from Walter de Gruyter. Please see www.degruyter.com for more information. Professor Puri is one of the most versatile and prolific researchers in the world in mathematical statistics. His research areas include nonparametric statistics, order statistics, limit theory under mixing, time series, splines, tests of normality, generalized inverses of matrices and related topics, stochastic processes, statistics of directional data, random sets, and fuzzy sets and fuzzy measures. His fundamental contributions in developing new rank-based methods and precise evaluation of the standard procedures, asymptotic expansions of distributions of rank statistics, as well as large deviation results concerning them, span such areas as analysis of variance, analysis of covariance, multivariate analysis, and time series, to mention a few. His in-depth analysis has resulted in pioneering research contributions to prominent journals that have substantial impact on current research. This book together with the other two volumes (Volume 1: Nonparametric Methods in Statistics and Related Topics; Volume 3: Time Series, Fuzzy Analysis and Miscellaneous Topics), are a concerted effort to make his research works easily available to the research community. The sheer volume of the research output by him and his collaborators, coupled with the broad spectrum of the subject matters investigated, and the great number of outlets where the papers were published, attach special significance in making these works easily accessible. The papers selected for inclusion in this work have been classified into three volumes each consisting of several parts. All three volumes carry a final part consisting of the contents of the other two, as well as the complete list of Professor Puri’s publications.

Table of Contents:
Preface Part I. LIMIT THEOREMS, RATES OF CONVERGENCE, AND RELATED TOPICS (INDEPENDENT CASE) Order of normal approximation for rank test statistics distribution Convergence and remainder terms in linear rank statistics Invariance principles for rank statistics for testing independence On the degeneration of the variance in the asymptotic normality of signed rank statistics On the order of magnitude of cumulants of von Mises functionals and related statistics On Berry–Esséen rates, a law of the iterated logarithm and an invariance principle for the proportion of the sample below the sample mean Cramér type large deviations for generalized rank statistics On the rate of convergence in the central limit theorem for signed rank statistics A sharpening of the remainder term in the higher-dimensional central limit theorem for multilinear rank statistics The order of normal approximation for signed linear rank statistics Central limit theorem for perturbed empirical distribution functions evaluated at a random point Limit theorems for random central order statistics Asymptotic expansions for sums of nonidentically distributed Bernoulli random variables On the rate of convergence in normal approximation and large deviation probabilities for a class of statistics On Hilbert-space-valued U-statistics On the central limit theorem in Hilbert space with application to U-statistics Asymptotic expansions in statistics: A review of methods and applications Normal approximation of U-statistics in Hilbert space Part II. LIMIT THEOREMS (DEPENDENT CASE) Empirical distribution functions and functions of order statistics for mixing random variables An invariance principle for processes indexed by two parameters and some statistical applications Limiting behavior of U-statistics, V -statistics, and one sample rank order statistics for nonstationary absolutely regular processes Weak invariance of generalized U-statistics for nonstationary absolutely regular processes The space ˜ Dk and weak convergence for the rectangle-indexed processes under mixing Weak invariance of the multidimensional rank statistic for nonstationary absolutely regular processe Weak convergence of the simple linear rank statistic under mixing conditions in the nonstationary case Weak convergence of weighted empirical U-statistics processes for dependent random variables Law of the iterated logarithm for perturbed empirical distribution functions evaluated at a random point for nonstationary random variables Valid Edgeworth expansions of M-estimators in regression models with weakly dependent residuals Conditional U-statistics for dependent random variables Weak convergence of sequences of first passage processes and applications Conditional empirical processes defined by nonstationary absolutely regular sequences Part III. EXTREME VALUE THEORY A strong invariance principle concerning the J -upper order statistics for stationary m-dependent sequences A strong invariance principle concerning the J -upper order statistics for stationary Gaussian sequences Extremes of Markov sequences Records and 2-block records of 1-dependent stationary sequences under local dependence