Linear algebra and linear models (Q5917685)

The book studies several aspects of statistical linear models by a linear algebraic approach. The basic aspects of the theory of linear estimation and testing statistical hypotheses of linear models are given. The necessary prerequisites, vector spaces and real matrices, multivariate normal distributions and distributions of quadratic forms, are developed. The generalized inverse and its applications are presented. Several results on eigenvalues, singular values, principal components and canonical correlations are emphasized. The linear model is used as the mathematical framework for experimental design. Optimality criteria are proposed to choose a design which has some desirable properties. In this sense, \(E\)-, \(A\)-, and \(D\)-optimality for a design and their statistical interpretations are presented. Some topics in generalized linear models are given. Some applications and exercises are also included.