# ESTIMATION, INFERENCE, AND SPECIFICATION TESTING FOR POSSIBLY MISSPECIFIED QUANTILE REGRESSION

Tae Hwan Kim, Halbert White

Research output: Chapter in Book/Report/Conference proceedingChapter

41 Citations (Scopus)

### Abstract

To date, the literature on quantile regression and least absolute deviation regression has assumed either explicitly or implicitly that the conditional quantile regression model is correctly specified. When the model is misspecified, confidence intervals and hypothesis tests based on the conventional covariance matrix are invalid. Although misspecification is a generic phenomenon and correct specification is rare in reality, there has to date been no theory proposed for inference when a conditional quantile model may be misspecified. In this paper, we allow for possible misspecification of a linear conditional quantile regression model. We obtain consistency of the quantile estimator for certain "pseudo-true" parameter values and asymptotic normality of the quantile estimator when the model is misspecified. In this case, the asymptotic covariance matrix has a novel form, not seen in earlier work, and we provide a consistent estimator of the asymptotic covariance matrix. We also propose a quick and simple test for conditional quantile misspecification based on the quantile residuals.

Original language English Maximum Likelihood Estimation of Misspecified Models Twenty Years Later 107-132 26 https://doi.org/10.1016/S0731-9053(03)17005-3 Published - 2003 Dec 1

### Publication series

Name Advances in Econometrics 17 0731-9053

### Fingerprint

Conditional quantiles
Inference
Quantile regression
Specification testing
Misspecification
Quantile
Covariance matrix
Estimator
Regression model
Asymptotic normality
Confidence interval
Deviation
Hypothesis test

### All Science Journal Classification (ASJC) codes

• Economics and Econometrics

### Cite this

Kim, T. H., & White, H. (2003). ESTIMATION, INFERENCE, AND SPECIFICATION TESTING FOR POSSIBLY MISSPECIFIED QUANTILE REGRESSION. In Maximum Likelihood Estimation of Misspecified Models: Twenty Years Later (pp. 107-132). (Advances in Econometrics; Vol. 17). https://doi.org/10.1016/S0731-9053(03)17005-3
Kim, Tae Hwan ; White, Halbert. / ESTIMATION, INFERENCE, AND SPECIFICATION TESTING FOR POSSIBLY MISSPECIFIED QUANTILE REGRESSION. Maximum Likelihood Estimation of Misspecified Models: Twenty Years Later. 2003. pp. 107-132 (Advances in Econometrics).
title = "ESTIMATION, INFERENCE, AND SPECIFICATION TESTING FOR POSSIBLY MISSPECIFIED QUANTILE REGRESSION",
abstract = "To date, the literature on quantile regression and least absolute deviation regression has assumed either explicitly or implicitly that the conditional quantile regression model is correctly specified. When the model is misspecified, confidence intervals and hypothesis tests based on the conventional covariance matrix are invalid. Although misspecification is a generic phenomenon and correct specification is rare in reality, there has to date been no theory proposed for inference when a conditional quantile model may be misspecified. In this paper, we allow for possible misspecification of a linear conditional quantile regression model. We obtain consistency of the quantile estimator for certain {"}pseudo-true{"} parameter values and asymptotic normality of the quantile estimator when the model is misspecified. In this case, the asymptotic covariance matrix has a novel form, not seen in earlier work, and we provide a consistent estimator of the asymptotic covariance matrix. We also propose a quick and simple test for conditional quantile misspecification based on the quantile residuals.",
author = "Kim, {Tae Hwan} and Halbert White",
year = "2003",
month = "12",
day = "1",
doi = "10.1016/S0731-9053(03)17005-3",
language = "English",
isbn = "0762310758",
pages = "107--132",
booktitle = "Maximum Likelihood Estimation of Misspecified Models",

}

Kim, TH & White, H 2003, ESTIMATION, INFERENCE, AND SPECIFICATION TESTING FOR POSSIBLY MISSPECIFIED QUANTILE REGRESSION. in Maximum Likelihood Estimation of Misspecified Models: Twenty Years Later. Advances in Econometrics, vol. 17, pp. 107-132. https://doi.org/10.1016/S0731-9053(03)17005-3
Maximum Likelihood Estimation of Misspecified Models: Twenty Years Later. 2003. p. 107-132 (Advances in Econometrics; Vol. 17).

Research output: Chapter in Book/Report/Conference proceedingChapter

TY - CHAP

T1 - ESTIMATION, INFERENCE, AND SPECIFICATION TESTING FOR POSSIBLY MISSPECIFIED QUANTILE REGRESSION

AU - Kim, Tae Hwan

AU - White, Halbert

PY - 2003/12/1

Y1 - 2003/12/1

N2 - To date, the literature on quantile regression and least absolute deviation regression has assumed either explicitly or implicitly that the conditional quantile regression model is correctly specified. When the model is misspecified, confidence intervals and hypothesis tests based on the conventional covariance matrix are invalid. Although misspecification is a generic phenomenon and correct specification is rare in reality, there has to date been no theory proposed for inference when a conditional quantile model may be misspecified. In this paper, we allow for possible misspecification of a linear conditional quantile regression model. We obtain consistency of the quantile estimator for certain "pseudo-true" parameter values and asymptotic normality of the quantile estimator when the model is misspecified. In this case, the asymptotic covariance matrix has a novel form, not seen in earlier work, and we provide a consistent estimator of the asymptotic covariance matrix. We also propose a quick and simple test for conditional quantile misspecification based on the quantile residuals.

AB - To date, the literature on quantile regression and least absolute deviation regression has assumed either explicitly or implicitly that the conditional quantile regression model is correctly specified. When the model is misspecified, confidence intervals and hypothesis tests based on the conventional covariance matrix are invalid. Although misspecification is a generic phenomenon and correct specification is rare in reality, there has to date been no theory proposed for inference when a conditional quantile model may be misspecified. In this paper, we allow for possible misspecification of a linear conditional quantile regression model. We obtain consistency of the quantile estimator for certain "pseudo-true" parameter values and asymptotic normality of the quantile estimator when the model is misspecified. In this case, the asymptotic covariance matrix has a novel form, not seen in earlier work, and we provide a consistent estimator of the asymptotic covariance matrix. We also propose a quick and simple test for conditional quantile misspecification based on the quantile residuals.

UR - http://www.scopus.com/inward/record.url?scp=33645021852&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=33645021852&partnerID=8YFLogxK

U2 - 10.1016/S0731-9053(03)17005-3

DO - 10.1016/S0731-9053(03)17005-3

M3 - Chapter

AN - SCOPUS:33645021852

SN - 0762310758

SN - 9780762310753
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