Based on the double penalized estimation method, a new variable selection procedure is proposed for partially linear models with longitudinal data. The proposed procedure can avoid the effects of the nonparametric estimator on the variable selection for the parameters components. Under some regularity conditions, the rate of convergence and asymptotic normality of the resulting estimators are established. In addition, to improve efficiency for regression coefficients, the estimation of the working covariance matrix is involved in the proposed iterative algorithm. Some simulation studies are carried out to demonstrate that the proposed method performs well.
Based on the empirical likelihood method, a testing procedure is proposed for polynomial regression models. Some simulations and a real data analysis are undertaken to investigate the power of the empirical likelihood based testing method.
Based on the empirical likelihood method, an instrumental variable based testing procedure is proposed for linear regression models with instrumental variables. The proposed testing method can attenuate the effect of endogeneity of covariates. Some simulations indicate that the proposed testing method is more powerful.
This paper considers the model testing for partially linear models with instrumental variables. By combining the instrumental variable method and the empirical likelihood method, an instrumental variable type testing procedure is proposed. The proposed testing procedure can attenuate the effect of endogeneity of covariates. Some simulations imply that the instrumental variable based empirical likelihood testing method is more poweful.
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