Optimal Bias Robust Regression Psi and Rho Revisited

17 Pages Posted: 12 Aug 2021

See all articles by Kjell Konis

Kjell Konis

University of Washington

R. Douglas Martin

University of Washington

Date Written: August 10, 2021

Abstract

Abstract This paper is focused on detailed aspects of the loss function rho and its derivative psi for an optimal bias robust regression method that minimizes the maximum asymptotic bias subject to a constraint on normal distribution efficiency. The analytic form of the psi function was discovered by Yohai and Zamar (1997), but the analytic form of the rho function was not known. Furthermore, the psi function has a curious feature of being equal to zero on an interval around the origin which forms a psi function “flat spot” whose length decreases with increasing normal distribution regression estimator efficiency, and is hardly noticeable in a plot of the psi function for 95% normal distribution efficiency. This paper focuses on the following aspects the optimal bias robust regression estimator: (1) The analytic form for the rho function; (2) A computational problem posed by the psi function flat spot and a solution to the problem using a slightly modified psi function that entails little loss of bias robustness; (3) A suite of functions available in an R package for computing the optimal psi and rho functions, and the modified psi and rho functions, for a specified normal distribution efficiency.

Keywords: Robust regression, bias robustness, eciency

JEL Classification: C13, C61

Suggested Citation

Konis, Kjell and Martin, R. Douglas, Optimal Bias Robust Regression Psi and Rho Revisited (August 10, 2021). Available at SSRN: https://ssrn.com/abstract=3902862 or http://dx.doi.org/10.2139/ssrn.3902862

Kjell Konis

University of Washington ( email )

Seattle, WA 98195
United States

R. Douglas Martin (Contact Author)

University of Washington ( email )

Applied Mathematics & Statistics
Seattle, WA 98195
United States

Do you have a job opening that you would like to promote on SSRN?

Paper statistics

Downloads
6
Abstract Views
76
PlumX Metrics