Multi-dimensional classification with semiparametric mixture model

Compared to non-model based classification methods, the model based classification has the advantage of classification together with regression analysis, and is the interest of our investigation. For robustness, we propose and study a semiparametric mixture model, in which each sub-density is only assumed unimodal. The semiparametric maximum likelihood estimate is used to estimate the parametric and nonparametric components. Then the Bayesian classification rule is used to classify the subjects according to the model. Large sample properties of the estimates are investigated, simulation studies are conducted to evaluate the finite sample performance of the proposed model, and then the method is applied to analyze a real data.