Weak Convergence of Randomly Weighted Dependent Residual Empiricals with Applications to Autoregression
随机加权依赖残差经验过程的弱收敛及自回归应用
This paper establishes the uniform closeness of a randomly weighted residual empirical process to its natural estimator via weak convergence techniques. The weights need not be independent, bounded or even square integrable. This result is used to yield the asymptotic uniform linearity of a class of rank statistics in $p$th-order autoregression models. The latter result, in turn, yields the asymptotic distributions of a class of robust and Jaeckel-type rank estimators. The…