A local likelihood approach to semiparametric inference

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The idea on localization of likelihood has been developed into statistical inference. This approach aims at combining parametric inference with nonparametric inference. A theoretical discussion on density estimation by mounting a kernel function into the likelihood function has been extensively established. Advantageous points of the local likelihood method over the usual plug-in density estimation and nonparametric density estimation are proven in both theoretical and experimental aspects. This approach is applied to the classification problem by kernel-weighting the classifier. Specifically the logistic regression discrimination is update to the localization version. The method automatically gives flexible nonlinality against the usual discriminant hyperplane. In principle it gives appropriate adjustment on the classifier to sample fluctuation by more weighting the likelihood function about data near the hypersurface and by less weighting that about data depart from the surface. It is observed that this idea on the localized classifier is closely related with the idea on the support vector machine in the field of neural networks. Now the close relation is focussed in order to propose the fusion of theses method.