A new robust quadratic discriminant function

Abstract

We propose a new quadratic discriminant function. It is devised based on the fact that eigenvalues of a sample covariance matrix are biased estimates of true eigenvalues. First, we rectify the biased eigenvalues. Then we construct a new covariance matrix whose eigenvalues are the rectified ones. Our quadratic discriminant function uses the covariance matrix. In a two-dimensional normal case, we show by a Monte Carlo method that our discriminant function works effectively, especially in the case of a small sample size.