SUT J. Math. 55 (2), 69-93, (December 2019) DOI: 10.55937/sut/1577359170
KEYWORDS: discriminant analysis, W classification statistic, location and scale mixtured expression, CPMC, High-dimensional asymptotic results, Upper confidence bounds on CPMC, 62H30, 62H12
This paper is concerned with -group linear discriminant analysis for multivariate normal populations with unknown mean vectors and unknown common covariance matrix for the case in which the sample sizes , and the dimension are large. We give Studentized version of the statistic under the high-dimensional asymptotic framework A1 that , , and tend to infinity together under the condition that converges to a constant in , and converges to a constant in . Asymptotic expansion of the distribution for the conditional probability of misclassification (CPMC) of the Studentized is derived under A1. By using this asymptotic expansion, we give the cut-off point such that the one of two CPMCs is less than the presetting value. Such the constrained discriminant rule is studied by Anderson (1973) and McLachlan (1977). Simulation result reveals that the proposed method is more accurate than McLachlan (1977)’s method for the case in which is relatively large.