On consistency factors and efficiency of robust S-estimators

• Marco Riani ^[2] ; Andrea Cerioli ^[2] ; Francesca Torti ^[1]
  1. [1] Joint Research Centre

     Joint Research Centre

     Arrondissement Brussel-Hoofdstad, Bélgica

     
  2. [2] Università di Parma
• Localización: Test: An Official Journal of the Spanish Society of Statistics and Operations Research, ISSN-e 1863-8260, ISSN 1133-0686, Vol. 23, Nº. 2, 2014, págs. 356-387
• Idioma: inglés
• DOI: 10.1007/s11749-014-0357-7
• Texto completo no disponible (Saber más ...)
• Resumen

  • We tackle the problem of obtaining the consistency factors of robust S-estimators of location and scale both in regression and multivariate analysis. We provide theoretical results, proving new formulae for their calculation and shedding light on the relationship between these factors and important statistical properties of S-estimators. We also give computational advances, suggesting efficient procedures so that hardly any time is lost for their calculation when computing S-estimates. In addition, when the purpose is to fix the efficiency of the scale estimator, we are able 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 this paper concentrates on S-estimates and Tukey’s Biweight and optimal loss functions, the main results can be easily extended to calculate the tuning consistency factors for other popular loss function and other robust estimators.