Higher order asymptotic theory for discriminant analysis in exponential families of distributions

This paper deals with the problem of classifying a multivariate observation X into one of two populations Π₁: p(x; w⁽¹⁾) ∈ S and Π₂: p(x; w⁽²⁾) ∈ S, where S is an exponential family of distributions and w⁽¹⁾ and w⁽²⁾ are unknown parameters. Let I; be a class of appropriate estimators (ŵ⁽¹⁾, ŵ⁽²⁾) of (w⁽¹⁾, w⁽²⁾ based on training samples. Then we develop the higher order asymptotic theory for a class of classification statistics D = [Ŵ