The Component Weighted Median Absolute Deviations Problem

Abstract

This paper considers the problem of robust modeling by using the well-known Least Absolute Deviation (LAD) regression. For that purpose, the approximation function is designed and analyzed, which is based on a certain component weight of the Weighted Median of Data. It is shown that the proposed approximation function is a piecewise constant function with finitely many pieces with respect to the model parameter. Thereby, an investigation of regions of constant values of the approximation function is conducted. It is established that the designed model based on the Component Weighted Median Absolute Deviations estimates a optimal model parameter on a finite set, which describes corresponding regions. Furthermore, the specified restriction of the approximation function is observed and analyzed, in order to examine the observed problem.