Interpretation and Semiparametric Efficiency in Quantile Regression under Misspecification

Ying-Ying Lee

Econometrics, 2015, vol. 4, issue 1, 1-14

Abstract: Allowing for misspecification in the linear conditional quantile function, this paper provides a new interpretation and the semiparametric efficiency bound for the quantile regression parameter ? ( ? ) in Koenker and Bassett (1978). The first result on interpretation shows that under a mean-squared loss function, the probability limit of the Koenker–Bassett estimator minimizes a weighted distribution approximation error, defined as \(F_{Y}(X'\beta(\tau)|X) - \tau\), i.e., the deviation of the conditional distribution function, evaluated at the linear quantile approximation, from the quantile level. The second result implies that the Koenker–Bassett estimator semiparametrically efficiently estimates the quantile regression parameter that produces parsimonious descriptive statistics for the conditional distribution. Therefore, quantile regression shares the attractive features of ordinary least squares: interpretability and semiparametric efficiency under misspecification.

Keywords: semiparametric efficiency bounds; misspecification; conditional quantile function; conditional distribution function; best linear approximation (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2015
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2225-1146/4/1/2/pdf (application/pdf)
https://www.mdpi.com/2225-1146/4/1/2/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jecnmx:v:4:y:2015:i:1:p:2-:d:61252

Access Statistics for this article

Econometrics is currently edited by Ms. Jasmine Liu

More articles in Econometrics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().