# Quantile Regression with Measurement Errors and Missing Data

Authored by: Ying Wei

# Handbook of Quantile Regression

Print publication date:  October  2017
Online publication date:  October  2017

Print ISBN: 9781498725286
eBook ISBN: 9781315120256

10.1201/9781315120256-11

#### Abstract

In many applications, data are imperfectly collected. Variables are often measured with error and data are missing for various reasons. When the covariates of interest, denoted here by x ${ \mathbf x }$ , are not directly observable and are, instead, measured with error, it is well known that such errors can lead to substantial attenuation of the estimated effects (Carroll et al., 2006). Likewise, ignoring missing observations in the data can lead to efficiency loss or biased estimation (Little, 2014). While there is an abundant literature on measurement errors and missing data, there have been little attention devoted to quantile methods directly, primarily due to the lack of parametric likelihood in quantile regression. In recent years, several methods have been developed specifically for quantile regression. In what follows, we review some methods dealing with measurement errors and missing data in quantile regression models.

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