Journal article
Oracle Estimation of a Change Point in High-Dimensional Quantile Regression
Journal of the American Statistical Association, Vol.113(523), pp.1184-1194
07/03/2018
DOI: 10.1080/01621459.2017.1319840
Abstract
In this article, we consider a high-dimensional quantile regression model where the sparsity structure may differ between two sub-populations. We develop ℓ
1
-penalized estimators of both regression coefficients and the threshold parameter. Our penalized estimators not only select covariates but also discriminate between a model with homogenous sparsity and a model with a change point. As a result, it is not necessary to know or pretest whether the change point is present, or where it occurs. Our estimator of the change point achieves an oracle property in the sense that its asymptotic distribution is the same as if the unknown active sets of regression coefficients were known. Importantly, we establish this oracle property without a perfect covariate selection, thereby avoiding the need for the minimum level condition on the signals of active covariates. Dealing with high-dimensional quantile regression with an unknown change point calls for a new proof technique since the quantile loss function is nonsmooth and furthermore the corresponding objective function is nonconvex with respect to the change point. The technique developed in this article is applicable to a general M-estimation framework with a change point, which may be of independent interest. The proposed methods are then illustrated via Monte Carlo experiments and an application to tipping in the dynamics of racial segregation. Supplementary materials for this article are available online.
Details
- Title: Subtitle
- Oracle Estimation of a Change Point in High-Dimensional Quantile Regression
- Creators
- Sokbae Lee - Columbia UniversityYuan Liao - Rutgers, The State University of New JerseyMyung Hwan Seo - Seoul National UniversityYoungki Shin - McMaster University
- Resource Type
- Journal article
- Publication Details
- Journal of the American Statistical Association, Vol.113(523), pp.1184-1194
- DOI
- 10.1080/01621459.2017.1319840
- ISSN
- 0162-1459
- eISSN
- 1537-274X
- Publisher
- Taylor & Francis
- Number of pages
- 11
- Grant note
- ERC-2014-CoG-646917-ROMIA / European Research Council (10.13039/501100000781)
- Language
- English
- Date published
- 07/03/2018
- Academic Unit
- Economics
- Record Identifier
- 9984936835202771
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