Statistical Estimation And Variable Selection For Semiparametric Models With Complex Data

In regression analysis, in purpose of simplify the models and improve the explanatory power of models, it is necessary to filter out the most important variables from numerous explanatory variables in regression analysis. This paper mainly studies the statistical estimation and variable selection of varying partially linear model with missing response and covariate measurement error. We use the imputation method to handle the missing data;"Correction for attenuation" method is applied to correct the measurement error in covariates. Combined with the SCAD punishment, the estimation of the parameters is proposed and the important variables are selected. It is also proved that under certain regular conditions the resulting estimations are consistent and the variable selection results with Oracle property. Numerical simulation was further implemented to discuss the limited sample properties of parameter estimation, simulation results show that this method can estimate the parameter very well and select the important variables efficiently.This paper also considered the estimation of varying coefficient partially linear models under covariate missing base on composite quantile regression. Inverse probability weighting method is applied to handle the missing covariate. The minimize problem of the composite quantile loss function was solves through MM algorithm. The numerical simulation results show that the estimation conducted by composite quantile regression is more efficient than least square estimation especially when the distribution of error is non-normal.