Interpretation and semiparametric efficiency in quantile regression under misspecification

Artikel

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 b(t) 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 FY(X'b(t)/X)-t, 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.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Journal: Econometrics ; ISSN: 2225-1146 ; Volume: 4 ; Year: 2016 ; Issue: 1 ; Pages: 1-14 ; Basel: MDPI

Classification and Topics

• Classification: Wirtschaft ; Semiparametric and Nonparametric Methods: General ; Single Equation Models; Single Variables: Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions
• Subject: semiparametric efficiency bounds ; misspecification ; conditional quantile function ; conditional distribution function ; best linear approximation

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Lee, Ying-Ying
• Event: Veröffentlichung
• (who): MDPI
• (where): Basel
• (when): 2016

Further information

• DOI: doi:10.3390/econometrics4010002
• Handle: http://hdl.handle.net/10419/171848
• Last update: 10.03.2025, 11:44 AM CET