This volume contains the invited papers and a selection of contributed papers which were presented at the 5th Tartu Conference on Multivariate Statistics and a one-day satellite workshop on matrices in statistics held in Estonia, May 1994. The papers have been grouped in six sections, which reflect the volume and range of the problems discussed during the conference. Each section opens with an invited lecture. The sections are: asymptotic distribution and expansions; general linear regression models; tests in multivariate statistics; multivariate non-parametric models and their applications; discrimination and classification; matrices in statistics. The book should be of interest to scientists in the field of probability and statistics.