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

Thomas Gueuning and Gerda Claeskens

No 538106, Working Papers of Department of Decision Sciences and Information Management, Leuven from KU Leuven, Faculty of Economics and Business (FEB), Department of Decision Sciences and Information Management, Leuven

Abstract: 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 SCAD, 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.

Keywords: High-dimensional data; Single-index model; Regularized estimation; Sparsity; Asymptotic normality; Confidence interval (search for similar items in EconPapers)
Date: 2016-04
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Published in FEB Research Report KBI_1611

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