TY - JOUR
T1 - Which robust versions of sample variance and sample covariance are most appropriate for econometrics
T2 - Symmetry-based analysis
AU - Sriboonchitta, Songsak
AU - Batyrshin, Ildar
AU - Kreinovich, Vladik
N1 - Publisher Copyright:
© 2016 by the Mathematical Association of Thailand. All rights reserved.
PY - 2016
Y1 - 2016
N2 - 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 |xi - â|from the (estimated) mean â. 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.
AB - 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 |xi - â|from the (estimated) mean â. 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.
KW - Robust statistics
KW - Sample covariance
KW - Sample variance
KW - Scale-invariance
UR - http://www.scopus.com/inward/record.url?scp=85008422675&partnerID=8YFLogxK
M3 - Artículo
SN - 1686-0209
VL - 14
SP - 37
EP - 50
JO - Thai Journal of Mathematics
JF - Thai Journal of Mathematics
IS - Special Issue appliedmathematics
ER -