Robust scale estimation under shifts in the mean. Issue 4 (4th July 2021)

• Record Type: Journal Article
• Authors: Axt, I.; Dürre, Alexander; Fried, Roland
• Is Part Of: Statistics. Volume 55:Issue 4(2021)
• Page Start: 787
• Page End: 830
• Publication Date: 2021-07-04
• Subjects: Blockwise estimation -- change-point -- outliers -- median absolute deviation; Mathematical statistics -- Periodicals; 519.505
• DOI: 10.1080/02331888.2021.1977812
• Languages: English
• ISSNs: 0233-1888

Abstract

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.