Outlier Detection in Regression Using an Iterated One-Step Approximation to the Huber-Skip Estimator

Soren Johansen and Bent Nielsen

Econometrics, 2013, vol. 1, issue 1, 1-18

Abstract: In regression we can delete outliers based upon a preliminary estimator and re-estimate the parameters by least squares based upon the retained observations. We study the properties of an iteratively defined sequence of estimators based on this idea. We relate the sequence to the Huber-skip estimator. We provide a stochastic recursion equation for the estimation error in terms of a kernel, the previous estimation error and a uniformly small error term. The main contribution is the analysis of the solution of the stochastic recursion equation as a fixed point, and the results that the normalized estimation errors are tight and are close to a linear function of the kernel, thus providing a stochastic expansion of the estimators, which is the same as for the Huber-skip. This implies that the iterated estimator is a close approximation of the Huber-skip.

Keywords: Huber-skip; iteration; one-step M-estimators; unit roots (search for similar items in EconPapers)
JEL-codes: B23 C C00 C01 C1 C2 C3 C4 C5 C8 (search for similar items in EconPapers)
Date: 2013
References: View references in EconPapers View complete reference list from CitEc
Citations: View citations in EconPapers (15)

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