Topics in statistical information theory (Q1095518)

This is a booklet about the cross entropy or the discrimination information for stochastic processes rather than for random variables. Hence, the results extend those in the book by the first author, Information theory and statistics (1959; Zbl 0088.104). Some of the potential applications are hypothesis testing and discrimination problems, for which the log-likelihood ratios associated with various stochastic processes are computed. A particular attention is paid to the linear discriminant functional and canonical correlations, whose computation is illustrated by a number of examples covering both continuous and discrete time processes. The book is somewhat terse, and many of the results are presented catalogue like with little effort to aid ones intuition. However, it is a useful collection of formulas with derivation, which the numerous examples illustrate.