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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.
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
- No. of pages:
- © Academic Press 1989
- 28th October 1989
- Academic Press
- eBook ISBN:
Center for multivariate Analysis, Department of statistics, The Pennsylvania State University.