Sign-Based Regression Quantiles

• Activity Number: 581
• Type: Contributed
• Date/Time: Wednesday, August 3, 2011 : 2:00 PM to 3:50 PM
• Sponsor: ENAR
• Author(s): Peter F. Tarassenko and Alexander Zhuravlev and Sergey Tarima*+
• Companies: Tomsk State University and Tomsk State University and Medical College of Wisconsin
• Keywords: quantile regression ; nonparameteric methods ; regression ; sign based procedures

Abstract

A sign-based (SB) approach suggests an alternative criterion for quantile regression (QR) fit. We generalize the well-known median regression SB procedure to the case of an arbitrary quantile level and compare it with the least absolute deviations (LAD) method. For linear models the SB criterion is a piecewise constant function and its minimization leads to one or several multidimensional polygons. We compare the mid-point of these polygons with the LAD estimator. Asymptotic properties of LAD and SB estimators are equivalent; however, there are finite sample differences as we show in a set of simulation scenarios. In many cases of QR parameter estimation the SB procedure demonstrates a significantly lower mean squared error (MSE) as compared to LAD based estimation. For small sample sizes (up to 10) the ratio of SB and LAD MSEs can come down to 0.5. For moderate sample sizes (near 50) the relative efficiency is typically around 0.95 in the presence of heteroscedasticity. The LAD shows lower than SB MSEs for distributions close to Laplace.