Confidence Intervals for High-Dimensional Partially Linear Single-Index Models

34 Pages Posted: 27 Apr 2016

See all articles by Thomas Gueuning

Thomas Gueuning

KU Leuven - Faculty of Business and Economics (FEB)

Gerda Claeskens

KU Leuven - Department of Economics

Date Written: April 2016

Abstract

We study partially linear single-index models where both model parts may contain highdimensional 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

Suggested Citation

Gueuning, Thomas and Claeskens, Gerda, Confidence Intervals for High-Dimensional Partially Linear Single-Index Models (April 2016). Available at SSRN: https://ssrn.com/abstract=2770528 or http://dx.doi.org/10.2139/ssrn.2770528

Thomas Gueuning (Contact Author)

KU Leuven - Faculty of Business and Economics (FEB) ( email )

Naamsestraat 69
Leuven, B-3000
Belgium

Gerda Claeskens

KU Leuven - Department of Economics ( email )

Leuven, B-3000
Belgium

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