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

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• 作者：Thomas Gueuning ^{thomas.gueuning@kuleuven.be" class="auth_mail" title="E-mail the corresponding author} ; Gerda Claeskens ; ^{gerda.claeskens@kuleuven.be" class="auth_mail" title="E-mail the corresponding author}
• 关键词：62F25 ; 62F12 ; 62G08 ; 62J07
• 刊名：Journal of Multivariate Analysis
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：149
• 期：Complete
• 页码：13-29
• 全文大小：513 K

文摘

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.