Zhao Zhibiao
Department of Statistics, Penn State University, University Park, Pennsylvania 16802, U.S.A.
Biometrika. 2011;98(1):81-90. doi: 10.1093/biomet/asq076.
We construct an asymptotic confidence interval for the mean of a class of nonstationary processes with constant mean and time-varying variances. Due to the large number of unknown parameters, traditional approaches based on consistent estimation of the limiting variance of sample mean through moving block or non-overlapping block methods are not applicable. Under a block-wise asymptotically equal cumulative variance assumption, we propose a self-normalized confidence interval that is robust against the nonstationarity and dependence structure of the data. We also apply the same idea to construct an asymptotic confidence interval for the mean difference of nonstationary processes with piecewise constant means. The proposed methods are illustrated through simulations and an application to global temperature series.
我们为一类具有恒定均值和时变方差的非平稳过程的均值构建了一个渐近置信区间。由于未知参数数量众多，基于通过移动块或非重叠块方法对样本均值的极限方差进行一致估计的传统方法并不适用。在块渐近等累积方差假设下，我们提出了一个自归一化置信区间，它对数据的非平稳性和相依结构具有稳健性。我们还应用相同的思想为具有分段常数均值的非平稳过程的均值差构建一个渐近置信区间。通过模拟和对全球温度序列的应用来说明所提出的方法。
