Asymptotic Properties of a Family of Minimum Quantile Distance Estimators
定义了一类基于M个指定分位数的最小化二次距离的估计量，证明了其一致性、渐近正态性和稳健性，并针对三参数对数正态分布计算了渐近相对效率，通过蒙特卡洛研究了小样本性质。
Abstract A family of estimators based upon M specified quantiles is defined. These procedures take as the estimate the vector that minimizes a quadratic distance measure between M sample quantiles and a parametric family of quantile functions. Under regularity conditions these estimators are consistent, asymptotically normal, and robust. For a specific quadratic form the estimator is optimal among a class of asymptotically normal estimators, and it approaches full efficiency as M approaches infinity. The asymptotic relative efficiency is computed for various sets of quantiles and various parameter values of the three-parameter lognormal distribution. The small-sample properties and robustness of the optimal M-quantile estimator for the three-parameter lognormal distribution are investigated in Monte Carlo studies.