Journal article
Oracle inequalities for sparse additive quantile regression in reproducing kernel Hilbert space
The Annals of statistics, Vol.46(2), pp.781-813
04/01/2018
DOI: 10.1214/17-AOS1567
Abstract
This paper considers the estimation of the sparse additive quantile regression (SAQR) in high-dimensional settings. Given the nonsmooth nature of the quantile loss function and the nonparametric complexities of the component function estimation, it is challenging to analyze the theoretical properties of ultrahigh-dimensional SAQR. We propose a regularized learning approach with a two-fold Lasso-type regularization in a reproducing kernel Hilbert space (RKHS) for SAQR. We establish nonasymptotic oracle inequalities for the excess risk of the proposed estimator without any coherent conditions. If additional assumptions including an extension of the restricted eigenvalue condition are satisfied, the proposed method enjoys sharp oracle rates without the light tail requirement. In particular, the proposed estimator achieves the minimax lower bounds established for sparse additive mean regression. As a by-product, we also establish the concentration inequality for estimating the population mean when the general Lipschitz loss is involved. The practical effectiveness of the new method is demonstrated by competitive numerical results.
Details
- Title: Subtitle
- Oracle inequalities for sparse additive quantile regression in reproducing kernel Hilbert space
- Creators
- Shaogao Lv - Nanjing Audit UniversityHuazhen Lin - City University of Hong KongHeng Lian - Southwestern University of Finance and EconomicsJian Huang - University of Iowa
- Resource Type
- Journal article
- Publication Details
- The Annals of statistics, Vol.46(2), pp.781-813
- Publisher
- INST MATHEMATICAL STATISTICS
- DOI
- 10.1214/17-AOS1567
- ISSN
- 0090-5364
- eISSN
- 2168-8966
- Number of pages
- 33
- Grant note
- KLAS-130026507 / Ministry of Education of China 11571282; 11528102 / National Natural Science Foundation of China JBK120509; 14TD0046 / Fundamental Research Funds for the Central Universities
- Language
- English
- Date published
- 04/01/2018
- Academic Unit
- Statistics and Actuarial Science
- Record Identifier
- 9984257745302771
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