Correcting MM estimates for "fat" data sets

• Autores: Maronna, Ricardo Antonio; Yohai, Victor Jaime
• Año de publicación: 2010
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: MM estimators; M-scale; HIgh-dimensional data
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

Regression MM estimates require the estimation of the error scale, and the determination of a constant that controls the efficiency. These two steps are based on the asymptotic results that are derived assuming that the number of predictors p remains fixed while the number of observations n tends to infinity, which means assuming that the ratio p/n is "small". However, many high-dimensional data sets have a "large" value of p/n (say, ≥0.2). It is shown that the standard asymptotic results do not hold if p/n is large; namely that (a) the estimated scale underestimates the true error scale, and (b) that even if the scale is correctly estimated, the actual efficiency can be much lower than the nominal one. To overcome these drawbacks simple corrections for the scale and for the efficiency controlling constant are proposed, and it is demonstrated that these corrections improve on the estimate's performance under both normal and contaminated data.
Fil: Maronna, Ricardo Antonio. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de La Plata. Facultad de Ciencias Exactas; Argentina
Fil: Yohai, Victor Jaime. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina