Rank procedures for some two-population multivariate extended classification problems

Given independent samples from three multivariate populations with cumulative distribution functions F(1)(x), F(2)(x), and F(0)(x) = [theta]F(1)(x) + (1 - [theta])F(2)(x), where 0 <= [theta] <= 1 is unknown, the three-action problem involving decision as to whether the value of [theta] is high, low, or intermediate, is considered. A class of consistent procedures based on the relative spacing of three sample averages of linearly compounded rank scores is formulated. The asymptotic operating characteristics of the procedures when F(1) and F(2) come close together are studied and the best choice of the compounding coefficients in terms of these considered. The consequence of using estimates of the best coefficients on the asymptotic operating characteristics is also examined.