期刊
JOURNAL OF COMPUTATIONAL AND GRAPHICAL STATISTICS
卷 22, 期 4, 页码 970-986出版社
TAYLOR & FRANCIS INC
DOI: 10.1080/10618600.2012.707454
关键词
Fused LASSO; Noncrossing; Oracle; Quantile regression; Smoothing; Sup-norm
资金
- NSF (National Science Foundation) [DMS-1007420]
- NSF [DMS-1005612]
- NIH (National Institute of Health) [P01-CA-142538]
- NSF CAREER Award [DMS-1149355]
- Division Of Mathematical Sciences
- Direct For Mathematical & Physical Scien [1149355] Funding Source: National Science Foundation
Conventional analysis using quantile regression typically focuses on fitting the regression model at different quantiles separately. However, in situations where the quantile coefficients share some common feature, joint modeling of multiple quantiles to accommodate the commonality often leads to more efficient estimation. One example of common features is that a predictor may have a constant effect over one region of quantile levels but varying effects in other regions. To automatically perform estimation and detection of the interquantile commonality, we develop two penalization methods. When the quantile slope coefficients indeed do not change across quantile levels, the proposed methods will shrink the slopes toward constant and thus improve the estimation efficiency. We establish the oracle properties of the two proposed penalization methods. Through numerical investigations, we demonstrate that the proposed methods lead to estimations with competitive or higher efficiency than the standard quantile regression estimation in finite samples. Supplementary materials for the article are available online.
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