A local likelihood approach to semiparametric inference

似然的局部化思想已发展为统计推断。该方法旨在将参数推理与非参数推理相结合。通过在似然函数中加入核函数进行密度估计的理论讨论已经被广泛地建立起来。从理论和实验两个方面证明了局部似然方法相对于通常的插入式密度估计和非参数密度估计的优越性。通过对分类器进行核加权，将该方法应用于分类问题。具体地说，Logistic回归判别是对本地化版本的更新。该方法针对通常的判别超平面自动给出灵活的非线性。原则上对分类器进行适当的调整，对超曲面附近数据的似然函数加权较大，对离面数据的似然函数加权较小，以适应样本的波动。可以看出，这种局部化分类器的思想与神经网络领域中的支持向量机思想有着密切的联系。现在着眼于这一密切关系，提出了将这些方法融合在一起。

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.