A Bootstrap Approach to Robust Regression
Dr. Hamadu Dallah

Abstract
We focus on the derivation of consistent estimates of the standard deviations of estimates of the parameters of a multiple regression model fitted via a robust procedure, namely, the so-called M (M for maximum likelihood) regression fitting method. M-regression is mostly actualized by way of weighted least squares (WLS). It is common knowledge that most commonly used statistical packages offering WLS assume that the weights are fixed. In this scenario M-regression yields standard errors that are inconsistent and unstable, moreso if the underlying sample is small. The alternative approach on offer in this article is the bootstrap. Using the re-sampling mechanism inherent in bootstrapping, it is demonstrated empirically that bootstrap standard errors are smaller than their M-regression counterparts.

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