Statistical Inferences For Varying Coefficient Partially Nonlinear Model With Missing Responses

Because of the flexibility of the semiparametric models,the varying coefficient partially nonlinear model has received a great deal of attention.In this paper,we consider statistical inferences for varying coefficient partially nonlinear model with missing responses.Firstly,based on the profile nonlinear least squares estimation of the complete data method,we impute a value for each missing response by the weighted method,then the profile nonlinear least squares estimation process is employed to estimate the unknown parameter and the nonparametric function,and the asymptotic normality of the resulting estimators is proved.Due to the advantages of the empirical likelihood method in constructing confidence region,we consider empirical likelihood inferences based on the weighted imputation method for the unknown parameter and nonparametric function,an empirical log-likelihood ratio function for the unknown parameter vector in the nonlinear function part and a residual-adjusted empirical log-likelihood ratio function for the nonparametric component are proposed,relevant confidence regions are also constructed.In addition,the response mean estimation is also studied,the normal approximated confidence intervals and empirical likelihood confidence intervals for the response mean are obtained.Finally,simulation studies are conducted to examine the finite sample performance of our methods,and the empirical likelihood approach based on the weighted imputation method(IEL)is further applied to a real data example.