# Collected Works of Jaroslav Hájek: With Commentary

# Collected Works of Jaroslav Hájek: With Commentary

ISBN: 978-0-470-85981-0 November 2000 696 Pages

## Description

"Hájek was undoubtedly a statistician of enormous power who, in his relatively short life, contributed fundamental results over a wide range of topics..." V. Barnett, University of Nottingham.

Hájek's writings in statistics are not only seminal but form a powerful unified body of theory. This is particularly the case with his studies of non-parametric statistics. His book "The Theory of Rank Test", with ?idák, was described by W. Hoeffding as almost the last word on the subject. Hájek's work still has great importance today, for example his research has proved highly relevant to recent investigations on bootstrap diagnostics. Much of Hájek's work is scattered through the literature and some of it quite inaccessible, existing only in the original Czech version. This book provides a valuable unified text of the collective works of Hájek with additional essays by internationally renowned contributors. Undoubtedly this book will be essential reading to modern researchers in nonparametric statistics.

Hájek's writings in statistics are not only seminal but form a powerful unified body of theory. This is particularly the case with his studies of non-parametric statistics. His book "The Theory of Rank Test", with ?idák, was described by W. Hoeffding as almost the last word on the subject. Hájek's work still has great importance today, for example his research has proved highly relevant to recent investigations on bootstrap diagnostics. Much of Hájek's work is scattered through the literature and some of it quite inaccessible, existing only in the original Czech version. This book provides a valuable unified text of the collective works of Hájek with additional essays by internationally renowned contributors. Undoubtedly this book will be essential reading to modern researchers in nonparametric statistics.

## Table of contents

HISTORICAL OVERVIEW.

Biography of Jaroslav Hájek.

Hájek and the Superefficiency Breakthrough.

Jaroslav Hájek and His Impact on the Theory of Rank Tests.

Recollection of My Contacts with Jaroslav Hájek.

On Some Early Papers of Jaroslav Hájek.

Contributions of Jaroslav Hájek to Statistical Inference on Stochastic Processes.

The Hájek Perspectives in Finite Population Sampling.

Publications of Jaroslav Hájek.

Hájek PhD Students.

COLLECTED WORKS OF JAROSLAV HÁJEK

Representative Cluster Sampling by a Method of Two Phases.

Some Rank Distributions and Their Applications.

Generalization of an Inequality of Kolmogorov.

Asymptotic Efficiency of a Certain Sequence of Tests.

Linear Estimation of the Mean Value of a Stationary Random Process with Convex Correlation Function.

Inequalities for the Generalized Student's Distribution and their Applications.

Predicting a Stationary Process when the Correlation Function is Convex.

A Property of J-Divergence of Marginal Probability Distributions.

On a Property of Normal Distributions of Any Stochastic Process.

On the Distribution of Some Statistics in the Presence of Intraclass Correlation.

On the Theory of Ratio Estimates.

Some Contributions to the Theory of Probability Sampling.

Optimum Strategy and Other Problems in Probability Sampling.

On a Simple Linear Model in Gaussian Processes.

Limiting Distributions in Simple Random Sampling from a Finite Population.

On Plane Sample and Related Geometrical Problems.

Some Extensions of the Wald-Wolfowitz-Noether Theorem.

On Linear Estimation Theory for an Infinite Number of Observations.

Concerning Relative Accuracy of Stratified and Systematic Sampling in a Plane.

On Linear Statistical Problems in Stochastic Processes.

An Inequality Concerning Random Linear Functionals on a Linear Space with a Random Norm and Its Statistical Application.

Asymptotically Most Powerful Rank-Order Tests.

Cost Minimization in Miltiparameter Estimation.

Asymptotic Theory of Rejective Sampling with Varying Probabilities from a Finite Population.

Extension of the Kolmogorov-Smirnov Test to Regression Alternatives.

On Basic Concepts of Statistics.

Locally Most Powerful Rank Tests of Independence.

Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives.

Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives II.

Miscellaneous Problems of Rank Test Theory.

A Characterization of Limiting Distributions of Regular Estimates.

Limiting Properties of Likelihoods and Inference.

Local Asymptotic Minimax and Admissibility in Estimation.

Asymptotic Sufficiency of the Vector of Ranks in the Bahadur Sense.

Regression Designs in Autoregressive Stochastic Processes.

Asymptotic Theories of Sampling with Varying Probabilities without Replacement.

Biography of Jaroslav Hájek.

Hájek and the Superefficiency Breakthrough.

Jaroslav Hájek and His Impact on the Theory of Rank Tests.

Recollection of My Contacts with Jaroslav Hájek.

On Some Early Papers of Jaroslav Hájek.

Contributions of Jaroslav Hájek to Statistical Inference on Stochastic Processes.

The Hájek Perspectives in Finite Population Sampling.

Publications of Jaroslav Hájek.

Hájek PhD Students.

COLLECTED WORKS OF JAROSLAV HÁJEK

Representative Cluster Sampling by a Method of Two Phases.

Some Rank Distributions and Their Applications.

Generalization of an Inequality of Kolmogorov.

Asymptotic Efficiency of a Certain Sequence of Tests.

Linear Estimation of the Mean Value of a Stationary Random Process with Convex Correlation Function.

Inequalities for the Generalized Student's Distribution and their Applications.

Predicting a Stationary Process when the Correlation Function is Convex.

A Property of J-Divergence of Marginal Probability Distributions.

On a Property of Normal Distributions of Any Stochastic Process.

On the Distribution of Some Statistics in the Presence of Intraclass Correlation.

On the Theory of Ratio Estimates.

Some Contributions to the Theory of Probability Sampling.

Optimum Strategy and Other Problems in Probability Sampling.

On a Simple Linear Model in Gaussian Processes.

Limiting Distributions in Simple Random Sampling from a Finite Population.

On Plane Sample and Related Geometrical Problems.

Some Extensions of the Wald-Wolfowitz-Noether Theorem.

On Linear Estimation Theory for an Infinite Number of Observations.

Concerning Relative Accuracy of Stratified and Systematic Sampling in a Plane.

On Linear Statistical Problems in Stochastic Processes.

An Inequality Concerning Random Linear Functionals on a Linear Space with a Random Norm and Its Statistical Application.

Asymptotically Most Powerful Rank-Order Tests.

Cost Minimization in Miltiparameter Estimation.

Asymptotic Theory of Rejective Sampling with Varying Probabilities from a Finite Population.

Extension of the Kolmogorov-Smirnov Test to Regression Alternatives.

On Basic Concepts of Statistics.

Locally Most Powerful Rank Tests of Independence.

Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives.

Asymptotic Normality of Simple Linear Rank Statistics Under Alternatives II.

Miscellaneous Problems of Rank Test Theory.

A Characterization of Limiting Distributions of Regular Estimates.

Limiting Properties of Likelihoods and Inference.

Local Asymptotic Minimax and Admissibility in Estimation.

Asymptotic Sufficiency of the Vector of Ranks in the Bahadur Sense.

Regression Designs in Autoregressive Stochastic Processes.

Asymptotic Theories of Sampling with Varying Probabilities without Replacement.