Consider the semiparametric varying-coefficient heteroscedastic partially linear model Yi = X^T i β＋ Z^T iα（Ti） ＋ σiei, 1 ≤ i≤ n, where σ ^2i= f（Ui）, β is a p × 1 column vector of unknown parameter, ...Consider the semiparametric varying-coefficient heteroscedastic partially linear model Yi = X^T i β＋ Z^T iα（Ti） ＋ σiei, 1 ≤ i≤ n, where σ ^2i= f（Ui）, β is a p × 1 column vector of unknown parameter, （Xi, Zi, Ti, Ui） are random design q-dimensional vector of unknown functions, el points, Yi are the response variables, α（-） is a are random errors. For both cases that f（.） is known and unknown, we propose the empirical log-likelihood ratio statistics for the parameter f（.）. For each case, a nonparametric version of Wilks＇ theorem is derived. The results are then used to construct confidence regions of the parameter. Simulation studies are carried out to assess the performance of the empirical likelihood method.展开更多
基金Supported by the National Natural Science Foundation of China (Grant No. 71171003)Natural Science Research Project of Anhui Provincial Colleges (Grant No. KJ2011A032)+3 种基金Anhui Polytechnic University Foundation for Recruiting Talent (Grant Nos. 2011YQQ0042009YQQ005)Young Teachers Science Research Foundation of Anhui Polytechnic University (Grant No. 2009YQ035)Anhui Provincial Natural Science Foundation
文摘Consider the semiparametric varying-coefficient heteroscedastic partially linear model Yi = X^T i β＋ Z^T iα（Ti） ＋ σiei, 1 ≤ i≤ n, where σ ^2i= f（Ui）, β is a p × 1 column vector of unknown parameter, （Xi, Zi, Ti, Ui） are random design q-dimensional vector of unknown functions, el points, Yi are the response variables, α（-） is a are random errors. For both cases that f（.） is known and unknown, we propose the empirical log-likelihood ratio statistics for the parameter f（.）. For each case, a nonparametric version of Wilks＇ theorem is derived. The results are then used to construct confidence regions of the parameter. Simulation studies are carried out to assess the performance of the empirical likelihood method.
