Relationships between maximum depth and projeccion regression estimates.

JORGE G. ADROVER, RICARDO A. MARONNA AND VICTOR J. YOHAI

JOURNAL OF STATISTICAL PLANNING AND INFERENCE

ELSEVIER SCIENCE BV

Año: 2002 vol. 105 p. 363 - 375

0378-3758

This article deals with the relationships between regression estimates based on projections (Ann. Statist. 21 (1993) 965) and on maximum depth (J. Amer. Statist. Assoc. 94 (1999) 388), which are shown to share the same basic idea. The maximum asymptotic bias of the latter is derived. A measure of residual smallness is de7ned, which turns out to be equivalent to depth. Two approximate algorithms based on subsampling are proposed to compute the maximum depth estimate: one based on the original de7nition, and the other on the new criterion. Finally, a Monte Carlo study is performed to compare the least median of squares estimate, the projection estimate, and the two approximate versions of the maximum depth estimate. It is seen that the latter have rather di<erent behaviors, and the best overall performance corresponds to the projection estimate and one of the versions of the depth estimate.