In many situations, it is crucial to estimate the variance properly. Ordinary variance estimators perform poorly in the presence of shifts in the mean. We investigate an approach based on non-overlapping blocks, which yields good results in change-point scenarios. We show the strong consistency and the asymptotic normality of such blocks-estimators of the variance under independence. Weak consistency is shown for short-range dependent strictly stationary data. We provide recommendations on the appropriate choice of the block size and compare this blocks-approach with difference-based estimators. If level shifts occur frequently and are rather large, the best results can be obtained by adaptive trimming of the blocks.

中文翻译：

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关于均值漂移下的方差估计

在许多情况下，正确估计方差至关重要。在均值存在偏差的情况下，普通方差估计量的效果较差。我们研究了一种基于非重叠块的方法，该方法在更改点方案中产生了良好的结果。我们展示了这种独立性下方差的块估计的强一致性和渐近正态性。对于短距离相关的严格平稳数据显示了弱一致性。我们提供的块大小选用合适的建议，并比较差基于估计这个块的方法。如果电平移位频繁发生并且相当大，则可以通过对块进行自适应修整来获得最佳结果。