Second-order expansion for the expected regret risk in classification of one-parametric distributions

Abstract

The plug-in rule is used for the classification of random observations into one of two regular one-parametric distributions. The maximum likelihood estimates of unknown parameters obtained from the stratified training sample are used. The second-order asymptotic expansion in terms of the inverses of the training sample sizes is derived for the expected regret risk. The closed-form expressions of the expansion coefficients are applicable for the performance evaluation of the proposed classification rule.