ON CONSISTENCY FACTORS AND EFFICIENCY OF ROBUST S-ESTIMATORS

The aim is to tackle the problem of obtaining the consistency factors of robust S-estimators of location and scale both in regression and multivariate analysis. Theoretical results are provided, proving new formulae for their calculation and shedding light on the relationship between these factors and important statistical properties of S-estimators. Computational advances are also given, suggesting efficient procedures which simply require the repeated computation of the inverse of the cdf of the Chi2 distribution so that hardly any time is lost to this calculation when computing S-estimates. In addition, when the purpose is to fix the efficiency of the scale estimator, it is possible to quantify to what extent the approximate algorithms which are currently available provide an acceptable solution, and when it is necessary to resort to the exact formulae. Finally, even if the work concentrates on S-estimates and Tukey’s biweight loss function, the main results can be easily extended to calculate the tuning consistency factors for other popular loss function and other robust estimators.

RIANI Marco;  CERIOLI Andrea;  TORTI Francesca; 

2014-08-19

CMStatistics

JRC87485

978-84-937822-3-8,   

https://publications.jrc.ec.europa.eu/repository/handle/JRC87485,