EFFICIENT REGRESSIONS VIA OPTIMALLY COMBINING QUANTILE INFORMATION
提出一种通过最优组合多个分位数信息来构建回归模型高效估计量的通用框架，适用于参数和非参数设定，理论证明其渐近方差可接近Cramér-Rao下界，蒙特卡洛实验显示优于现有方法。
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 non-regular 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.