ON THE MISCLASSIFICATION BY A LINEAR DISCRIMINATION OF A CONTAMINATED MULTI-VARIATE NORMAL DISTRIBUTION

This paper discusses the linear discrimination of the following multi-variate normal model:\Pi_i:(1-\alpha) N\left(\mu_i, \Sigma\right)+\alpha N\left(\mu_i, k^2 \Sigma\right), \quad i=1,2 where, is the contamination rate （0≤α≤1）, ∑, k² the scale parameters, and the location parameters μ₁,μ₂ may be assumed unknown. It gives out the asymptotic distributions of two kinds of oonditional, and one kind of unoonditional misclassification rates. Please refer to Theorems 1 and 2 for the definite forms of the asymptotic distributions and the misclassification rates.