Multivariate Statistical Inference is a 10-chapter text that covers the theoretical and applied aspects of multivariate analysis, specifically the multivariate normal distribution using the invariance approach. Chapter I contains some special results regarding characteristic roots and vectors, and partitioned submatrices of real and complex matrices, as well as some special theorems on real and complex matrices useful in multivariate analysis. Chapter II deals with the theory of groups and related results that are useful for the development of invariant statistical test procedures, including the Jacobians of some specific transformations that are useful for deriving multivariate sampling dis...
Vector and matrix algebra; Groups and Jacobian of some transformations; Multivariate distributions and Invariance; Properties of multivariate distributions; Estimators of parameters and their functions; Basic multivariate sampling distributions; Tests of hypotheses of mean vectors; Tests concerning covariance matrices and mean vectors; Discriminant analysis; Principal components; Canonical correlations; Factor analysis.
In applied and pure sciences, the structural properties of groups are increasingly utilised to find better solutions in statistical sciences. Modern computers make statistical methods with large numbers of variables feasible. Invariance is a mathematical term for symmetry, and many statistical problems exhibit such properties. In statistical analysis with large numbers of variables, the invariance approach is becoming increasingly popular and useful because of its ability and usefulness in deriving better statistical procedures.In this book, Multivariate Statistical Inference is presented through Invariance.
Beginning with the historical background of probability theory, this thoroughly revised text examines all important aspects of mathematical probability - including random variables, probability distributions, characteristic and generating functions, stochatic convergence, and limit theorems - and provides an introduction to various types of statistical problems, covering the broad range of statistical inference.;Requiring a prerequisite in calculus for complete understanding of the topics discussed, the Second Edition contains new material on: univariate distributions; multivariate distributions; large-sample methods; decision theory; and applications of ANOVA.;A primary text for a year-long undergraduate course in statistics (but easily adapted for a one-semester course in probability only), Introduction to Probability and Statistics is for undergraduate students in a wide range of disciplines-statistics, probability, mathematics, social science, economics, engineering, agriculture, biometry, and education.
General concepts of probability; Random variables, probability distributions, and characteristics functions; Stochastic convergence and limit theorems; Contents of statistics; Order statistics and related distributions; Statistical inference - parametric point estimation; Testing to statistical hypotheses; Sequential analysis; Nonparametric methods; The general linear hypothesis and analysis of variance.