Asymptotic expansions for the moments of the regret risk of classification based on mixed variables (Q2769674)

The aim of the present article is to obtain general expansions of expected regret risk, using the maximum likelihood estimates of unknown parameters for the distributions of mixed feature variables. More precisely, a sample-based rule is obtained from the Bayes classification rule by replacing unknown parameters by maximum likelihood estimates from the training sample. Then, the sample-based rule is used for the classification of random observations of mixed feature variables (for appropriate regularity conditions). The general asymptotic expansions for the expectation and variance of the regret risk for different parametric structures are derived, in order to evaluate the performance of the proposed classification rule, and to obtain the optimal training sample allocation when minimizing the asymptotic expected regret risk.NEWLINENEWLINEFor the entire collection see [Zbl 0968.00043].