Multivariate Statistics and Probability

Essays in Memory of Paruchuri R. Krishnaiah

C. R. Rao, M. M. Rao

• Publisher: Academic Press
• Year: 2014
• Print ISBN: 9780125802055
• eBook ISBN: 9781483263830
• Topic: Mathematics
• Subtopic: Applied Mathematics
• Index: Mathematics

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

• Front Cover
• Multivariate Statistics and Probability
• Copyright Page
• Table of Contents
• Contributors
• Preface
• In Memoriam
• Chapter 1. Joint Asymptotic Distribution of Marginal Quantiles and Quantile Functions in Samples from a Multivariate Population
• Chapter 2. Kernel Estimators of Density Function of Directional Data
• Chapter 3. On Determination of the Order of an Autoregressive Model
• Chapter 4. Admissible Linear Estimation in a General Gauss-Markov Model with an Incorrectly Specified Dispersion Matrix
• Chapter 5. On Moment Conditions for Valid Formal Edgeworth Expansions
• Chapter 6. Ergodicity and Central Limit Theorems for a Class of Markov Processes
• Chapter 7. Conditionally Ordered Distributions
• Chapter 8. A Discounted Cost Relationship
• Chapter 9. Strong Consistency of M-Estimates in Linear Models
• Chapter 10. Minimal Complete Classes of Invariant Tests for Equality of Normal Covariance Matrices and Sphericity
• Chapter 11. Invariance Principles for Changepoint Problems
• Chapter 12. On the Area of the Circles Covered by a Random Walk
• Chapter 13. Normed Likelihood as Saddlepoint Approximation
• Chapter 14. Non-uniform Error Bounds for Asymptotic Expansions of Scale Mixtures of Distributions
• Chapter 15. Empirical and Hierarchical Bayes Competitors of Preliminary Test Estimators in Two Sample Problems
• Chapter 16. On Confidence Bands in Nonparametric Density Estimation and Regression
• Chapter 17. A Note on Generalized Gaussian Random Fields
• Chapter 18. Smoothness Properties of the Conditional Expectation in Finitely Additive White Noise Filtering
• Chapter 19. Equivariant Estimation of a Mean Vector µ of N(µ, ∑) with µ'∑-1µ=1 or ∑-1/2µ=c or ∑=σ2µ'µl
• Chapter 20. A Generalized Cauchy-Binet Formula and Applications to Total Positivity and Majorization
• Chapter 21. Isotonic M-Estimation of Location: Union-Intersection Principle and Preliminary Test Versions
• Chapter 22. Some Asymptotic Inferential Problems Connected with Elliptical Distributions
• Chapter 23. Stochastic Integrals of Empirical-Type Processes with Applications to Censored Regression
• Chapter 24. Nonminimum Phase Non-Gaussian Deconvolution
• Chapter 25. Inference in a Model with at Most One Slope-Change Point
• Chapter 26. Maximum Likelihood Principle and Model Selection when the True Model Is Unspecified
• Chapter 27. An Asymptotic Minimax Theorem of Order n–1/2
• Chapter 28. An Improved Estimation Method for Univariate Autoregressive Models
• Chapter 29. Paradoxes in Conditional Probability
• Chapter 30. Inference Properties of a One-Parameter Curved Exponential Family of Distributions with Given Marginals
• Chapter 31. Asymptotically Precise Estimate of the Accuracy of Gaussian Approximation in Hubert Space
• Chapter 32. The Estimation of the Bispectral Density Function and the Detection of Periodicities in a Signal
• Chapter 33. Analysis of Odds Ratios in 2×n Ordinal Contingency Tables
• Chapter 34. Asymptotic Expansions of the Distributions of Some Test Statistics for Gaussian ARMA Processes
• Chapter 35. Estimating Multiple Rater Agreement for a Rare Diagnosis
• Author Index
• Subject Index