Confidence intervals for high-dimensional partially linear single-index models

JOURNAL OF MULTIVARIATE ANALYSIS

卷:149

Article

Claeskens, Gerda¹ 

[1] Katholieke Univ Leuven, Fac Econ & Business, ORSTAT, Naamsestr 69, B-3000 Leuven, Belgium

关键词: High-dimensional data;    Single-index model;    Regularized estimation;    Sparsity;    Asymptotic normality;    Confidence interval;   

DOI  :  10.1016/j.jmva.2016.03.007

来源: Elsevier

【 摘 要 】

We study partially linear single-index models where both model parts may contain high dimensional variables. While the single-index part is of fixed dimension, the dimension of the linear part is allowed to grow with the sample size. Due to the addition of penalty terms to the loss function in order to provide sparse estimators, such as obtained by lasso or smoothly clipped absolute deviation, the construction of confidence intervals for the model parameters is not as straightforward as in the classical low-dimensional data framework. By adding a correction term to the penalized estimator a desparsified estimator is obtained for which asymptotic normality is proven. We study the construction of confidence intervals and hypothesis tests for such models. The simulation results show that the method performs well for high-dimensional single-index models. (C) 2016 Elsevier Inc. All rights reserved.

【 授权许可】

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