Probability Theory and Extreme Value Theory
Volume 2: Probability Theory and Extreme Value Theory
Published on 2. December 2003
Book
Hardback
754 pages
978-90-6764-385-6 (ISBN)
Description
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.
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.
More details
Edition
Reprint 2011
Language
English
Place of publication
Zeist
Netherlands
Publishing group
Brill
Target group
US School Grade: College Graduate Student
Dimensions
Height: 230 mm
Width: 155 mm
Weight
1721 gr
ISBN-13
978-90-6764-385-6 (9789067643856)
Copyright in bibliographic data and cover images is held by Nielsen Book Services Limited or by the publishers or by their respective licensors: all rights reserved.
Schweitzer Classification
Other editions
Additional editions
Madan Lal Puri | Peter G. Hall | Marc Hallin
Probability Theory and Extreme Value Theory
E-Book
07/2011
1st Edition
De Gruyter Mouton
€389.00
Available for download
Madan Lal Puri | Peter G. Hall | Marc Hallin
Madan Lal Puri: Selected Collected Works / Probability Theory and Extreme Value Theory
Book
01/2003
1st Edition
De Gruyter Mouton
€579.00
Article exhausted; check different version
Complete work / Part of the work
Douglas C. Hall | Marc Hallin | George Roussas
Madan LaL Puri. Selected Collected Works (3 vols)
Set Volumes 1-3
Book
07/2003
VSP International Science Publishers
€966.50
Article is exhausted; no reprint
Content
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-Esseen rates, a law of the iterated logarithm and an invariance principle for the proportion of the sample below the sample mean
Cramer 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
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-Esseen rates, a law of the iterated logarithm and an invariance principle for the proportion of the sample below the sample mean
Cramer 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