On linear lon-odds and estimation of discriminant coefficients

Fisher's Linear Discriminant Function Can be used to classify an individual who has sampled from one of two multivariate normal Populations. In the following, this function is viewed as the other given his data vector it is assumed that the Population means and common covariance matrix are unknown. The vector of discriminant coeffients β(p×1) is the gradient of posterior log-odds and certain of its lineqar functions are directional derivatives which have a practical meaning. Accordingly, we treat the problems of estimating several linear functions of β The usual estimatoes of these functions are scaled versions of the unbiased estmators. In this Paper, these estimators are domainated by explicit alterenatives under a quadratic loss function. we reduce the problem of estimating β to that of estimating the inverse convariance matrix.