Multidimensional Statistics: Gaussian Linear Models

The book outlines the statistics of Gaussian, i.e., normally distributed, random variables which is the most developed to date. The core of the book is the general theory of multidimensional linear models, represented geometrically. It examines as one single whole their specific forms (dispersion analysis, regression analysis) which used to be studied separately. The mathematical apparatus is based on the modules over rings of square matrices endowed with matrix-valued scalar multiplication. For multidimensional data, this structure replaces vector algebra. The correlation theory is expounded based on linear models and the new concept of matrix correlation, The reader is expected to have a good knowledge of mathematical analysis, linear algebra and the basics of probability theory and mathematical statistics.

The book may be useful to anyone who is interested in mathematical statistics, especially, to students and graduate students of mathematical and economic faculties.

The book can form the basis of a one-term lecture course.