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In this article, we consider the statistical inferences for varying coefficient partially non linear model with missing covariates. The purpose of this article is two-fold. First, we propose an inverse probability weighted profile non linear least squares technique for estimating the unknown parameter and the non parametric function, and the asymptotic normality of the resulting estimators are proved. Second, we consider empirical likelihood inferences for the unknown parameter and non parametric function. The empirical log-likelihood ratio function for the unknown parameter vector in the non linear function part and a residual-adjusted empirical log-likelihood ratio function for the non parametric component are proposed. The corresponding Wilks phenomena are obtained and the confidence regions for the parameter and the point-wise confidence intervals for coefficient function are constructed. Simulation studies and real data analysis are conducted to examine the finite sample performance of the proposed methods. [ABSTRACT FROM AUTHOR]

Varying coefficient partially linear models are usually used for longitudinal data analysis, and an interest is mainly to improve efficiency of regression coefficients. By the orthogonality estimation technology and the empirical likelihood inference method, we propose a new orthogonality-based empirical likelihood inference method to estimate parameter and nonparametric components in a class of varying coefficient partially linear instrumental variable models with longitudinal data. The proposed procedure can separately estimate the parametric and nonparametric components, and the resulting estimators do not affect each other. Under some mild conditions, we establish some asymptotic properties of the resulting estimators. Furthermore, the finite sample performance of the proposed procedure is assessed by some simulation experiments and a real data analysis. [ABSTRACT FROM AUTHOR]

In this article, empirical likelihood inferences for the varying coefficient partially nonlinear models are investigated. 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. The corresponding Wilks phenomena are proved and the confidence regions for parametric component and nonparametric component are constructed. Simulation studies indicate that, in terms of coverage probabilities and average areas of the confidence regions, the empirical likelihood method performs better than the normal approximation-based method. Furthermore, a real data set application is also provided to illustrate the proposed empirical likelihood estimation technique. [ABSTRACT FROM AUTHOR]

In this article, we consider empirical likelihood inference for the parameter in the additive partially linear models when the linear covariate is measured with error. By correcting for attenuation, a corrected-attenuation empirical log-likelihood ratio statistic for the unknown parameter β, which is of primary interest, is suggested. We show that the proposed statistic is asymptotically standard chi-square distribution without requiring the undersmoothing of the nonparametric components, and hence it can be directly used to construct the confidence region for the parameter β. Some simulations indicate that, in terms of comparison between coverage probabilities and average lengths of the confidence intervals, the proposed method performs better than the profile-based least-squares method. We also give the maximum empirical likelihood estimator (MELE) for the unknown parameter β, and prove the MELE is asymptotically normal under some mild conditions. [ABSTRACT FROM AUTHOR]