Which Robust Versions of Sample Variance and Sample Covariance Are Most Appropriate for Econometrics: Symmetry-Based Analysis

Authors

Songsak Sriboonchitta, Chiang Mai UniversityFollow
Ildar Batyrshin, Instituto Politécnico NacionalFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

5-2016

Comments

Technical Report: UTEP-CS-16-25a

Abstract

In many practical situations, we do not know the shape of the corresponding probability distributions and therefore, we need to use robust statistical techniques, i.e., techniques that are applicable to all possible distributions. Empirically, it turns out the the most efficient robust version of sample variance is the average value of the p-th powers of the deviations |x_i- a| from the (estimated) mean a. In this paper, we use natural symmetries to provide a theoretical explanation for this empirical success, and to show how this optimal robust version of sample variance can be naturally extended to a robust version of sample covariance.