Single Index Quantile Regression for Heteroscedastic Data

• Activity Number: 650
• Type: Contributed
• Date/Time: Thursday, August 13, 2015 : 8:30 AM to 10:20 AM
• Sponsor: Section on Nonparametric Statistics
• Author(s): Eliana Christou*
• Companies: Penn State
• Keywords: quantile regression ; single index model ; non-iterative algorithm ; Nadaraya-Watson estimator

Abstract

Quantile regression (QR) has become a popular method of data analysis since conditional quantiles is of interest in many scientific studies. As a result, linear and nonlinear QR models have been studied extensively. Recently the single index QR (SIQR) model has received some attention. Compared to the single index mean regression problem, the fitting and the asymptotic theory of the SIQR model are more complicated due to the lack of closed form expressions for estimators of conditional quantiles. Consequently, the proposed methods are necessarily iterative.

We propose a non-iterative estimation algorithm. The estimator is shown to be consistent, and its asymptotic distribution is derived under heteroscedasticity. In addition, the present work differs from the existing literature in terms of the parametrization used to ensure identifiability of the parametric vector. Instead of the usual constraint, we assume that the first coefficient is 1 and estimate the remaining d-1 coefficients. This distinction is more than simply cosmetic as it affects, in a critical way, the correspondence between the estimator derived and the asymptotic theory. Simulations confirm the asymptotic results.