Conditional Quantile Estimators: A Small Sample Theory

Grigory Franguridi, Bulat Gafarov and Kaspar Wüthrich

No 9046, CESifo Working Paper Series from CESifo

Abstract: 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.

Keywords: 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 (search for similar items in EconPapers)
JEL-codes: C21 C26 (search for similar items in EconPapers)
Date: 2021
New Economics Papers: this item is included in nep-ore
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (1)

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