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


Inf

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

Ratings and Reviews