Jackknife Empirical Likelihood For Semiparametric Partially Linear Index Models

The semiparametric partially linear index model contains many commonly used parametric models,semiparametric models and nonparametric models such as,lin-ear regression models,partial linear regression models and generalized partial lin-ear regression models.Therefore,this model has been widely used in the fields of statistics and economics.In this thesis,we propose a novel jackknife empirical like-lihood method for the regression coefficients of the semiparametric partially linear index model.Firstly,based on the rank estimation of the regression coefficients in Abrevaya&Shin(2011),we obtain a U-statistic by smoothing this estimation.Sec-ondly,we apply the jackknife empirical likelihood method to this U-statistic,under certain conditions,we prove that the proposed jackknife empirical likelihood ratio asymptotically converges to the chi-squared distribution.Based on this result,we can construct the confidence region for the regression coefficients.Finally,extensive simulation studies and real data analysis are also conducted,which show the effec-tiveness of the proposed method.