Bent Line Quantile Regression with Application to an Allometric Study of Land Mammals' Speed and Mass

• Activity Number: 36
• Type: Contributed
• Date/Time: Sunday, August 1, 2010 : 2:00 PM to 3:50 PM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Chenxi Li*+ and Ying Wei and Rick Chappell and Xuming He
• Companies: University of Wisconsin-Madison and Columbia University and University of Wisconsin-Madison and University of Illinois at Urbana-Champaign
• Keywords: Bahadur representation ; Bootstrap ; Change-point ; Piecewise linear ; Profile estimation ; Quantile regression

Abstract

We consider quantile regression in the situation where the conditional quantile function of the response variable is piecewise linear but still continuous in one of the covariates and linear in others. To analyze such data, we propose a bent line quantile regression model. We obtain its parameter estimates via profile estimation, prove that the estimates have asymptotic normality given the existence of a change-point, and discuss several methods for testing the existence of a change-point in bent line quantile regression together with a power comparison by simulation. An example of land mammal maximal running speeds is given to illustrate an application of bent line quantile regression in which this model is theoretically justified and its parameters are of direct biological interest.