Efficient Quantile Regression for Linear Heterogeneous Models

• Activity Number: 360
• Type: Contributed
• Date/Time: Tuesday, August 2, 2011 : 10:30 AM to 12:20 PM
• Sponsor: Business and Economic Statistics Section
• Author(s): Yoonsuh Jung*+ and Yoonkyung Lee and Steven N. MacEachern
• Companies: The University of Texas MD Anderson Cancer Center and The Ohio State University and The Ohio State University
• Keywords: check loss function ; heteroscedasticity ; quantile regression

Abstract

Quantile regression provides estimates of a range of conditional quantiles. This stands in contrast to traditional regression techniques, which focus on a single conditional mean function. Lee et al. (2009) proposed efficient quantile regression by rounding the sharp corner of the loss. The main modification generally involves an asymmetric L2 adjustment of the loss function around zero. The adjustment leads to superior finite sample performance by exploiting the bias-variance tradeoff. We extend the idea of L2 adjusted quantile regression to two linear heterogeneous models. The first model involves a set of weights in quantile regression (as in one description of weighted least squares). The second incorporates location-scale model, which introduces different weights and is preferable due to an invariance argument. We discuss several choices of reasonable weights that can be practically useful. Finally, the L2 adjustment is constructed to diminish as sample size grows. Conditions to retain consistency properties are provided.