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EFFICIENT REGRESSIONS VIA OPTIMALLY COMBINING QUANTILE INFORMATION

Published online by Cambridge University Press:  06 June 2014

Zhibiao Zhao  and
Zhijie Xiao
Zhibiao Zhao
Affiliation:
Penn State University
Zhijie Xiao*
Affiliation:
Boston College
*
*Address correspondence to Zhijie Xiao, Department of Economics, Boston College, Chestnut Hill, MA 02467, USA and Shandong University, China; e-mail: zhijie.xiao@bc.edu.
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Abstract

We develop a generally applicable framework for constructing efficient estimators of regression models via quantile regressions. The proposed method is based on optimally combining information over multiple quantiles and can be applied to a broad range of parametric and nonparametric settings. When combining information over a fixed number of quantiles, we derive an upper bound on the distance between the efficiency of the proposed estimator and the Fisher information. As the number of quantiles increases, this upper bound decreases and the asymptotic variance of the proposed estimator approaches the Cramér–Rao lower bound under appropriate conditions. In the case of nonregular statistical estimation, the proposed estimator leads to super-efficient estimation. We illustrate the proposed method for several widely used regression models. Both asymptotic theory and Monte Carlo experiments show the superior performance over existing methods.

Type
ARTICLES
Information
Econometric Theory , Volume 30 , Issue 6 , December 2014 , pp. 1272 - 1314
Copyright
Copyright © Cambridge University Press 2014 

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