Efficient regressions via optimally combining quantile information

Zhibiao Zhao, Zhijie Xiao

Research output: Contribution to journalArticlepeer-review

68 Scopus citations


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.

Original languageEnglish (US)
Pages (from-to)1272-1314
Number of pages43
JournalEconometric Theory
Issue number6
StatePublished - Apr 29 2014

All Science Journal Classification (ASJC) codes

  • Social Sciences (miscellaneous)
  • Economics and Econometrics


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