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In this paper, we propose a new approach to the empirical likelihood inference for the parameters in heteroscedastic partially linear single-index models. In the growing dimensional setting, it is proved that estimators based on semiparametric efficient score have the asymptotic consistency, and the limit distribution of the empirical log-likelihood ratio statistic for parameters (β⊤,θ⊤)⊤ is a normal distribution. Furthermore, we show that the empirical log-likelihood ratio based on the subvector of β is an asymptotic chi-square random variable, which can be used to construct the confidence interval or region for the subvector of β. The proposed method can naturally be applied to deal with pure single-index models and partially linear models with high-dimensional data. The performance of the proposed method is illustrated via a real data application and numerical simulations. [ABSTRACT FROM AUTHOR]

We apply empirical likelihood (EL) for high-dimensional semiparametric models and propose penalized empirical likelihood (PEL) method for parameter estimation and variable selection. It is shown that the estimator based on EL has the asymptotic consistent property, and that the limit distribution of the EL ratio statistic for the parameters θ is asymptotic normal distribution. Furthermore, in a high-dimensional setting, we prove that PEL in semiparametric models has the oracle property, that is, with probability tending to 1 , the estimator based on PEL for the nonzero coefficients is efficient. Moreover, the PEL ratio statistic for the parameters θ is a χ q 2 distribution under the true null hypothesis. The performance of the proposed method is illustrated via a real data application and numerical simulations. [ABSTRACT FROM AUTHOR]