标题： 强混合数据和截尾数据的乘积极限与分位数过程的高斯逼近 显示英文标题

标题： Strong Gaussian approximations of product-limit and Quantile Processes for Strong mixing and censored data

摘要： 本文中，我们考虑在右删失相依数据下未知分位数函数的乘积限分位数估计量。这是一个与利用乘积限方法估计未知分布函数平行的问题。构造了乘积限过程和乘积限分位数过程同时强高斯逼近，逼近速率为 $O((\log n)^{-\lambda})$ 对某些 $\lambda>0,$。然后将乘积限过程的强高斯逼近应用于推导乘积限过程的重对数律。 显示英文摘要

摘要： In this paper, we consider the product-limit quantile estimator of an unknown quantile function under a censored dependent model. This is a parallel problem to the estimation of the unknown distribution function by the product-limit estimator under the same model. Simultaneous strong Gaussian approximations of the product-limit process and product-limit quantile process are constructed with rate $O((\log n)^{-\lambda})$ for some $\lambda>0,$. The strong Gaussian approximation of the product-limit process is then applied to derive the laws of the iterated logarithm for product-limit process.