High Dimensional Inference in Partially Linear Models

Content Provider	Scilit
Author	Zhu, Ying Yu, Zhuqing Cheng, Guang
Copyright Year	2017
Description	Journal: SSRN Electronic Journal We propose two semiparametric versions of the debiased Lasso procedure for the model $Y_{i}$ = $X_{i}β_{0}$ + $g_{0}(Z_{i}$) + $ε_{i}$, where $β_{0}$ is high dimensional but sparse (exactly or approximately). Both versions are shown to have the same asymptotic normal distribution and do not require the minimal signal condition for statistical inference of any component in $β_{0}$. Our method also works when $Z_{i}$ is high dimensional provided that the function classes $𝔼(X_{ij}|Z_{i}$)s and $𝔼(Y_{i}|Z_{i}$) belong to exhibit certain sparsity features, e.g., a sparse additive decomposition structure. We further develop a simultaneous hypothesis testing procedure based on multiplier bootstrap. Our testing method automatically takes into account of the dependence structure within the debiased estimates, and allows the number of tested components to be exponentially high.
Related Links	http://arxiv.org/pdf/1708.02564 https://papers.ssrn.com/sol3/Delivery.cfm?abstractid=3015397
ISSN	10914358
e-ISSN	15565068
DOI	10.2139/ssrn.3015397
Journal	SSRN Electronic Journal
Language	English
Publisher	Elsevier BV
Publisher Date	2017-08-08
Access Restriction	Open
Subject Keyword	Journal: SSRN Electronic Journal Statistics and Probability High Dimensional
Content Type	Text
Resource Type	Article
Subject	Public Health, Environmental and Occupational Health Psychiatry and Mental Health