Some tests with unbalanced data from a bivariate normal population

Abstract

SummaryLet (X, Y) follow a bivariate normal distribution, N2(/~,/~, a~, a], p). In this paper, we have considered the problems of testing hypotheses H0,:/~=0, H02:/l~=/~ and H03: p=O on the basis of an unbalanced data set-up consisting of nl paired observations, n2 additional observations on X only and n3 additional observations on Y only. Some new tests are proposed.