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Abstract:
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It is known that a pre-specified parametric model is efficient if the model is correctly specified, but not robust against miss-specification; and that the nonparametric method is robust but not efficient. In practice often some parametric model is known to work well for the normal group, but not sure sub-distribution the abnormal group. We propose and study a semiparametric model in this setting for multi-dimensional classification problem. The model is mixture with a known component and an unknown component, the semiparametric maximum likelihood estimate is used to estimate the model parameter and the unknown density. Then we use the Neyman-Pearson classification rule to classify the subjects according to this semiparametric model. Large sample properties of this method is investigated, and simulation studies conducted to evaluate the performance of the proposed model, and it will be applied to the classification procedures in the Social Security Administration disability program.
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