Intervals Which Leave the Minimum Sum of Absolute Errors Regression Unchanged

Subhash C. Narula, Vince A. Sposito and John F. Wellington

Journal of the Royal Statistical Society Series C, 1993, vol. 42, issue 2, 369-378

Abstract: One of the appealing properties of the minimum sum of absolute errors (MSAE) regression is its resistance to outliers and long‐tailed error distributions. Just like the sample median, the MSAE estimators are influenced by all the observations but determined by only a subset of the observations. The MSAE estimates are not altered if the value of the response (or predictor) variable for an observation associated with a non‐O residual is within a certain interval. In this paper we develop procedures to determine such intervals for the simple linear regression model.

Date: 1993
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