Robust scale estimation under shifts in the mean

Abstract

In many applications the standard deviation of the observations needs to be estimated, e.g., for standardization. In the presence of outliers and jumps in the mean suitable estimation procedures are required, since ordinary scale estimators are biased in such situations. We propose a modification of the median absolute deviation (MAD) based on segregating the data into many non-overlapping blocks, which performs well in the outlier and change-point scenario, as can be seen in a simulation study. Theoretical results, such as strong consistency and asymptotic normality, are shown. Moreover, suggestions on the choice of the block size are given. We compare the performance of the proposed estimation procedure with that of other robust estimation techniques.

Keywords:

• Blockwise estimation
• change-point
• outliers
• median absolute deviation

Acknowledgments

We are grateful to the editors and the referees for their helpful and constructive comments.

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work has been supported by the Collaborative Research Center ‘Statistical modeling of nonlinear dynamic processes’ (SFB 823) of the German Research Foundation (DFG) which is gratefully acknowledged.