@techreport{Horowitz2006Nonparametric,
abstract = {We consider nonparametric estimation of a regression function that is identified by requiring a specified quantile of the regression error conditional on an instrumental variable to be zero. The resulting estimating equation is a nonlinear integral equation of the first kind, which generates an ill-posed-inverse problem. The integral operator and distribution of the instrumental variable are unknown and must be estimated nonparametrically. We show that the estimator is mean-square consistent, derive its rate of convergence in probability, and give conditions under which this rate is optimal in a minimax sense. The results of Monte Carlo experiments show that the estimator behaves well in finite samples.},
address = {London},
author = {Joel Horowitz and Sokbae Lee},
copyright = {http://www.econstor.eu/dspace/Nutzungsbedingungen},
doi = {10.1920/wp.cem.2006.0906},
keywords = {C13; C31; 330; Statistical inverse , endogenous variable , instrumental variable , optimal rate , nonlinear integral equation , nonparametric regression},
language = {eng},
number = {CWP09/06},
publisher = {Centre for Microdata Methods and Practice (cemmap)},
title = {Nonparametric instrumental variables estimation of a quantile regression model},
type = {cemmap working paper},
url = {http://hdl.handle.net/10419/79400},
year = {2006}
}