Strong Consistency of Regression Quantiles and Related Empirical Processes
研究了线性模型中回归分位数统计量的强相合性，在误差独立同分布及设计序列和误差分布的温和正则条件下成立，并建立了相关经验分位数过程的强相合性及条件分布函数估计的Glivenko-Cantelli型定理。
The strong consistency of regression quantile statistics (Koenker and Bassett [4]) in linear models with iid errors is established. Mild regularity conditions on the regression design sequence and the error distribution are required. Strong consistency of the associated empirical quantile process (introduced in Bassett and Koenker [1]) is also established under analogous conditions. However, for the proposed estimate of the conditional distribution function of Y, no regularity conditions on the error distribution are required for uniform strong convergence, thus establishing a Glivenko-Cantelli-type theorem for this estimator.