题 目: Difference-based Estimation for Semi-parametric Varying -coefficient Partially Linear Models
演讲人: Qingfeng Liu, Otaru University of Commerce
主持人：隋勇 博士
时 间: 2010年3月23日 (周二) 3:30-5:00pm
地 点: 上海交通大学北楼103
Abstract
The varying-coefficient partially linear model (VCPLM) is a mixture of the varying-coefficient model (VCM) and partially linear model (PLM). It improves over both of them in terms of flexibility. It allows the coefficient of the nonlinear component to vary according to some additional variables so that the model is flexible enough to express complicated real-world phenomena. In addition VCPLM can alleviate the so-called "curse of dimensionality" of VCM. This paper targets at the asymptotic properties of the differenced based estimator (DBE) for the linear components of VCPLM. Regularity conditions for asymptotic normality of DBE are derived. We further show that when the difference order q grows to infinity with the sample size n, the efficiency of the estimator can be improved by choosing appropriate weights. We propose a type of optimal weight matrix, spike and compund spike weights. We call such spike and compund spike weights optimal weights because the efficiency of the DBE can not be improved anymore by using other weight matrix. A plug-in method is provided for estimating the non-parametric component and its convergence rate is provided. The compound spike weight is applied to some simulation experiments and real data to demonstrate its finite-sample performance.
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