Some problems of statistical inference in regression and discriminant analysis

Abstract

In this dissertation the following problems I the area of regression and discriminant analysis have been discussed. (1) Suppose there are m groups or populations and the regression lines of y on k independent variables x₁,..., x(subscript k) in these m groups are concurrent, the problem of statistical inference about this point of concurrence is investigated. Exact tests of significance for the goodness of fit of a proposed point of concurrence and departure from concurrence have been derived. (2) Discrimination between two multivariate populations π₁ and π₂ can be done with the same discriminant function as that between π₃ and π₄ if the vector of mean difference between π₁ and π₂ is proportional to the vector mean difference between π₃ and π₄. A likelihood ratio test is derived for testing this hypothesis. (3) The problem of analysis of association between two attributes A and B in a contingency table can be handled with the help of canonical analysis of two vectors. Whether this association is linear or not and if it is linear, whether a proposed set of scores are adequate for this purpose can be tested by using the classical multivariate criteria like Wilks' λ, Pillai's V, Hotelling generalized T²(subscript o). Pillai's V and Hotelling's T²(subscript o) have not yet been considered in the literature. This is done in this discretion.