Conditional Quantile Estimators: A Small Sample Theory

Arbeitspapier

We study the small sample properties of conditional quantile estimators such as classical and IV quantile regression. First, we propose a higher-order analytical framework for comparing competing estimators in small samples and assessing the accuracy of common inference procedures. Our framework is based on a novel approximation of the discontinuous sample moments by a Hölder-continuous process with a negligible error. For any consistent estimator, this approximation leads to asymptotic linear expansions with nearly optimal rates. Second, we study the higher-order bias of exact quantile estimators up to O (1/n). Using a novel non-smooth calculus technique, we uncover previously unknown non-negligible bias components that cannot be consistently estimated and depend on the employed estimation algorithm. To circumvent this problem, we propose a “symmetric” bias correction, which admits a feasible implementation. Our simulations confirm the empirical importance of bias correction.

Object Details

• Language: Englisch

References and Relationships

• Bibliographic citation: Series: CESifo Working Paper ; No. 9046

Classification and Topics

• Classification: Wirtschaft ; Single Equation Models; Single Variables: Cross-Sectional Models; Spatial Models; Treatment Effect Models; Quantile Regressions ; Single Equation Models: Single Variables: Instrumental Variables (IV) Estimation
• Subject: non-smooth estimators ; KMT coupling ; Hungarian construction ; higher-order asymptotic distribution ; higher-order stochastic expansion ; order statistic ; bias correction ; mixed integer linear programming (MILP) ; exact estimators ; k-step estimators ; quantile

Contributors, Places and Time

• Event: Geistige Schöpfung
• (who): Franguridi, Grigory ; Gafarov, Bulat ; Wüthrich, Kaspar
• Event: Veröffentlichung
• (who): Center for Economic Studies and Ifo Institute (CESifo)
• (where): Munich
• (when): 2021

Further information

• Handle: http://hdl.handle.net/10419/235416
• Last update: 10.03.2025, 11:45 AM CET