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Estimation and variable selection in partially linear models for massive data has been discussed by several authors. However, there does not seem to exist an established procedure for other semiparametric models, such as the semiparametric varying-coefficient linear model, the single index regression model, the partially linear errors-in-variables model, etc. In this paper, we propose a general procedure for variable selection in high-dimensional general semiparametric models by penalized semiparametric estimating equations. Under some regularity conditions, the oracle property is established, which the number of parameters is allowed to diverge. Furthermore, we also propose a split-and-conquer variable selection procedure for high-dimensional general semiparametric models with massive data. Under some weak regularity conditions, we establish the oracle property of the proposed procedure when the number of subsets does not grow too fast. What is more, the split-and-conquer procedure enjoys the oracle property as the penalized estimator by using all the dataset, and can substantially reduce computing time and computer memory requirements. The performance of the proposed method is illustrated via a real data application and numerical simulations. [ABSTRACT FROM AUTHOR]

In this paper, we apply empirical likelihood for two-sample problems with growing high dimensionality. Our results are demonstrated for constructing confidence regions for the difference of the means of twop-dimensional samples and the difference in value between coefficients of twop-dimensional sample linear model. We show that empirical likelihood based estimator has the efficient property. That is, asp→ ∞ for high-dimensional data, the limit distribution of the EL ratio statistic for the difference of the means of two samples and the difference in value between coefficients of two-sample linear model is asymptotic normal distribution. Furthermore, empirical likelihood (EL) gives efficient estimator for regression coefficients in linear models, and can be as efficient as a parametric approach. The performance of the proposed method is illustrated via 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]