Linear statistical inference and its applications

  title={Linear statistical inference and its applications},
  author={Calyampudi R. Rao},
Algebra of Vectors and Matrices. Probability Theory, Tools and Techniques. Continuous Probability Models. The Theory of Least Squares and Analysis of Variance. Criteria and Methods of Estimation. Large Sample Theory and Methods. Theory of Statistical Inference. Multivariate Analysis. Publications of the Author. Author Index. Subject Index. 

Theory of multivariate statistics

Linear algebra.- Random vectors.- Gamma, Dirichlet, and F distributions.- Invariance.- Multivariate normal.- Multivariate sampling.- Wishart distributions.- Tests on mean and variance.- Multivariate

Applied Multivariate Analysis

Introduction.- Vector and Matrix Algebra.- The Multivariate Normal Distribution, Multivariate Normality, and Covariance Structure.- One- and Two-Sample Tests.- Multivariate Analysis of Variance.-

Probability Limits, Asymptotic Distributions, and Properties of Maximum Likelihood Estimators

The purpose of this chapter is to introduce certain basic results from probability and statistical theory. A thorough understanding of such results is quite essential to those wishing a complete

Estimation of variance components and applications

Matrix Algebra. Asymptotic Distribution of Quadratic Statistics. Variance and Covariance Components Models. Identifiability and Estimability. Minimum Norm Quadratic Estimation. Pooling of Information

Mathematical Statistics: Exercises and Solutions

Probability Theory.- Fundamentals of Statistics.- Unbiased Estimation.- Estimation in Parametric Models.- Estimation in Nonparametric Models.- Hypothesis Tests.- Confidence Sets.

Statistical inference on stationary random fields

Statistical methods are developed to model random processes on multidimensional Euclidean space from observed data and algorithms are described for fitting parametric models and testing between alternative model structures.

Multiple population covariance structure analysis under arbitrary distribution theory

This paper states and proves the asymptotic properties of constrained generalized least squares estimators in the analysis of covariance structures in multiple populations with arbitrary

Robustness of statistical inference in factor analysis and related models

SUMMARY A class of latent variable models which includes the unrestricted factor analysis model is considered. It is shown that minimum discrepancy test statistics and estimators derived under

Applications of Estimators of a Density and its Derivatives to Certain Statistical Problems

SUMMARY Several statistical problems are considered. By reducing them to problems of estimating functionals of a density, derivatives of a density, or both, a method of finding partial solutions is

Nonparametric Methods in Longitudinal Studies

Abstract Inference procedures based on some simple rank statistics are proposed and studied for the statistical analysis of longitudinal data. These robust and asymptotically efficient procedures do