Efficient Influence Function of the Coefficient Functions in Quantile Regression

• Activity Number: 26
• Type: Contributed
• Date/Time: Sunday, August 3, 2014 : 2:00 PM to 3:50 PM
• Sponsor: IMS
• Author(s): Hiroyuki Taniai*+
• Companies: Waseda University
• Keywords: Quantile Regression ; semiparametrics ; efficient inference

Abstract

As in Koenker and Xiao (2006, JASA), the Quantile Regression model has an interpretation as a Random Coefficient Regression model where the coefficients are function of uniform random variables. In this paper, we regard this model as a kind of Mixture model by looking at the covariate as a "random nuisance parameter" whose distribution serves as a mixing distribution. So this can be seen as a infinite-dimensional version of Pfanzagl (1982), Chapter 14. Consequently I derive the tangent space for the coefficient functions (infinite-dimensional), and then present the form of efficient influence function for a fixed probability as well. This, together with the Donsker result for the Regression Quantile Process indexed by the probability values, will yield a basis of the efficient inference for the coefficients as functions.