Date of Award
Doctor of Philosophy
Theoretical developments in multivariate analysis are primarily based on the assumption of multivariate normality and very little is known for other cases. The aim of the present work is to generalize results of multivariate analysis based on a class of elliptic distributions, more specifically the subclass of the multivariate t-distributions with suitable parameters, rather than the usual normality assumption. The multivariate normal distribution belongs to the class of elliptic as well as the subclass of t-distribution.;The major contributions of the thesis are: (a) An elliptic set-up for uncorrelated samples is proposed. (b) The distributions of sample mean and covariance matrix are derived. (c) Classification problem is studied for the elliptic set-up.;The elliptic class is further specialized to a subclass of multivariate t-distributions, whose characteristic function, conditional distributions etc. are derived. Also the above problems (b) and (c) are studied. In addition the following problems have been solved: (i) null and non-null distributions of quadratic forms (analogue of non-central chi-square). (ii) estimation of location, scale and degrees of freedom parameters of the t-distribution and the sampling properties of the estimators. (iii) orthogonal factor analysis when both observed error and unobserved factors follow multivariate t-distributions. (iv) estimation of parameters and testing of hypothesis for a regression model with error variable having a multivariate t-distribution.
Sutradhar, Brajendra Chandra, "Contributions To Multivariate Analysis Based On Elliptic T Model" (1984). Digitized Theses. 1382.