This book presents recent non-asymptotic results for approximations in
multivariate statistical analysis. The book is unique in its focus on
results with the correct error structure for all the parameters
involved. Firstly, it discusses the computable error bounds on
correlation coefficients, MANOVA tests and discriminant functions
studied in recent papers. It then introduces new areas of research in
high-dimensional approximations for bootstrap procedures, Cornish-Fisher
expansions, power-divergence statistics and approximations of statistics
based on observations with random sample size. Lastly, it proposes a
general approach for the construction of non-asymptotic bounds,
providing relevant examples for several complicated statistics. It is a
valuable resource for researchers with a basic understanding of
multivariate statistics.