The goal of this paper is to indicate a new method for constructing normal confidence intervals for the mean, when the data is coming from stochastic structures with possibly long memory, especially when the dependence structure is not known or even the existence of the density function. More precisely we introduce a random smoothing suggested by the kernel estimators for the regression function. Applications are presented to linear processes and reversible Markov chains with long memory.

中文翻译：

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依赖均值的新稳健置信区间

本文的目的是指出一种新方法，用于构建均值的正态置信区间，当数据来自可能具有长记忆的随机结构时，尤其是当相关结构未知或什至不存在密度函数时。更准确地说，我们引入了由回归函数的核估计器建议的随机平滑。应用程序介绍了线性过程和具有长记忆的可逆马尔可夫链。