Multivariate Statistics and Probability - 1st Edition - ISBN: 9780125802055, 9781483263830

Multivariate Statistics and Probability

1st Edition

Essays in Memory of Paruchuri R. Krishnaiah

Editors: C. R. Rao M. M. Rao
eBook ISBN: 9781483263830
Imprint: Academic Press
Published Date: 28th October 1989
Page Count: 582
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Description

Multivariate Statistics and Probability: Essays in Memory of Paruchuri R. Krishnaiah is a collection of essays on multivariate statistics and probability in memory of Paruchuri R. Krishnaiah (1932-1987), who made significant contributions to the fields of multivariate statistical analysis and stochastic theory. The papers cover the main areas of multivariate statistical theory and its applications, as well as aspects of probability and stochastic analysis. Topics range from finite sampling and asymptotic results, including aspects of decision theory, Bayesian analysis, classical estimation, regression, and time-series problems.

Comprised of 35 chapters, this book begins with a discussion on the joint asymptotic distribution of marginal quantiles and quantile functions in samples from a multivariate population. The reader is then introduced to kernel estimators of density function of directional data; moment conditions for valid formal edgeworth expansions; and ergodicity and central limit theorems for a class of Markov processes. Subsequent chapters focus on minimal complete classes of invariant tests for equality of normal covariance matrices and sphericity; normed likelihood as saddlepoint approximation; generalized Gaussian random fields; and smoothness properties of the conditional expectation in finitely additive white noise filtering.

This monograph should be of considerable interest to researchers as well as to graduate students working in theoretical and applied statistics, multivariate analysis, and random processes.

Table of Contents


Preface

Contributors

In Memoriam

Joint Asymptotic Distribution of Marginal Quantiles and Quantile Functions in Samples from a Multivariate Population

Kernel Estimators of Density Function of Directional Data

On Determination of the Order of an Autoregressive Model

Admissible Linear Estimation in a General Gauss-Markov Model with an Incorrectly Specified Dispersion Matrix

On Moment Conditions for Valid Formal Edgeworth Expansions

Ergodicity and Central Limit Theorems for a Class of Markov Processes

Conditionally Ordered Distributions

A Discounted Cost Relationship

Strong Consistency of M-Estimates in Linear Models

Minimal Complete Classes of Invariant Tests for Equality of Normal Covariance Matrices and Sphericity

Invariance Principles for Changepoint Problems

On the Area of the Circles Covered by a Random Walk

Normed Likelihood as Saddlepoint Approximation

Non-uniform Error Bounds for Asymptotic Expansions of Scale Mixtures of Distributions

Empirical and Hierarchical Bayes Competitors of Preliminary Test Estimators in Two Sample Problems

On Confidence Bands in Nonparametric Density Estimation and Regression

A Note on Generalized Gaussian Random Fields

Smoothness Properties of the Conditional Expectation in Finitely Additive White Noise Filtering

Equivariant Estimation of a Mean Vector μ of N(μ,Σ) with 'Σ-1=1 or Σ-1/2μ=c or Σ = σ2μ'μ1

A Generalized Cauchy—Binet Formula and Applications to Total Positivity and Majorization

Isotonic M-Estimation of Location: Union-Intersection Principle and Preliminary Test Versions

Some Asymptotic Inferential Problems Connected with Elliptical Distributions

Stochastic Integrals of Empirical-Type Processes with Applications to Censored Regression

Nonminimum Phase Non-Gaussian Deconvolution

Inference in a Model with at Most One Slope-Change Point

Maximum Likelihood Principle and Model Selection when the True Model is Unspecified

An Asymptotic Minimax Theorem of Order n-1/2

An Improved Estimation Method for Univariate Autoregressive Models

Paradoxes in Conditional Probability

Inference Properties of a One-Parameter Curved Exponential Family of Distributions with Given Marginals

Asymptotically Precise Estimate of the Accuracy of Gaussian Approximation in Hubert Space

The Estimation of the Bispectral Density Function and the Detection of Periodicities in a Signal

Analysis of Odds Ratios in 2xn Ordinal Contingency Tables

Asymptotic Expansions of the Distributions of Some Test Statistics for Gaussian ARMA Processes

Estimating Multiple Rater Agreement for a Rare Diagnosis

Author Index

Subject Index

Details

No. of pages:
582
Language:
English
Copyright:
© Academic Press 1989
Published:
Imprint:
Academic Press
eBook ISBN:
9781483263830

About the Editor

C. R. Rao

Affiliations and Expertise

Center for multivariate Analysis, Department of statistics, The Pennsylvania State University.

M. M. Rao