Mathematical problems in management

Simple proof of robustness for the least trimmed squares estimator in linear regression models

A. S. Shvedov

National Research University "Higher School of Economics" (HSE), Moscow

Abstract: Pointed out is that in classical linear regression model the residuals are assumed to be normally distributed with zero average and standard deviation. However, the real data usually do not satisfy the classical model assumptions. At the same time, even a single outlier can influence significantly on regression parameters estimation. One of the robust regression methods with high breakdown point is the method of least trimmed squares. The new proof of the breakdown point estimation theorem is given, being much more simple that the classic proof.

Keywords: robust regression, least trimmed squares estimator, breakdown point.

UDC: 519.233