Quantile Regression Estimates For A Class Of Linear And Partially Linear Errors-In-Variables Models

We consider the problem of estimating quantile regression coefficients in errorsin -variables models. When the error variables for both the response and the manifest variables have a joint distribution that is spherically symmetric but otherwise unknown, the regression quantile estimates based on orthogonal residuals are shown to be consistent and asymptotically normal. We also extend the work to partially linear models when the response is related to some additional covariate. Key Words and Phrases: Kernel, linear regression, semiparametric model, errors-in-variables, regression quantile. Corresponding Author: Xuming He, Department of Statistics, University of Illinois, 725 S. Wright, Champaign, IL 61820. Email: x-he@uiuc.edu. 1 INTRODUCTION Regression analysis is routinely carried out in all areas of statistical applications. It helps explain how a dependent variable Y relates to independent variables X. Most authors consider the estimation or inference problems based on data o..