Asymptotic Matrix Methods

The exact distributions of multivariate statistics used for the inference in multivariate analysis are usually not known or quite difficult to handle. The topic of this book belongs to the area of approximation of unknown distributions through classical distributions and to the related estimation problems. The methods used here are based on concepts of matrix algebra like the Kronecker product, the vec-operator and the matrix derivative. The multivariate normal distribution and the class of elliptical distributions are examined. The asymptotic variance of the sample correlation coefficient is calculated using approximate linearization. Some applications of the asymptotic distribution of the sample correlation coefficient are considered for populations with different distributions. The main term of the bias of the shape parameter of the asymmetric normal distribution and the Läuter's F-statistic was found using the Taylor expansion. Simulation experiments are described and the results of the simulation study are presented beside derivation of theoretical results.

Autorentext

Born: July 25, 1974, Kohtla-Järve, Estonia.Academic degree:PhD in Mathematical Statistics.Date and Site of Obtaining Degree:October 2003, University of Tartu, Estonia.Professional employment:1997-2003 Lecturer and since 2003 Associate Professor in Virumaa College of Tallinn University of Technology, Estonia.