Interquantile Shrinkage in Regression Models.

TitleInterquantile Shrinkage in Regression Models.
Publication TypeJournal Article
Year of Publication2013
AuthorsJiang, Liewen, Huixia Judy Wang, and Howard D. Bondell
JournalJ Comput Graph Stat
Date Published2013

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 towards 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. Supplemental materials for the article are available online.

Alternate JournalJ Comput Graph Stat
Original PublicationInterquantile shrinkage in regression models.
PubMed ID24363546
PubMed Central IDPMC3867140
Grant ListP01 CA142538 / CA / NCI NIH HHS / United States