On scale estimation under shifts in the mean

Abstract

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 this change-point scenario. We show the strong consistency and the asymptotic normality of such blocks-estimators of the variance under rather general conditions. For estimation of the standard deviation a blocks-estimator based on average standard deviations turns out to be preferable over the square root of the average variances. We provide recommendations on the appropriate choice of the block size and compare this blocks-approach with difference-based estimators. If level shifts occur rather frequently even better results can be obtained by adaptive trimming of the blocks under the assumption of normality.