Breakdown points of t-type regression estimators

Citation
Xm. He et al., Breakdown points of t-type regression estimators, BIOMETRIKA, 87(3), 2000, pp. 675-687
Citations number
26
Categorie Soggetti
Biology,Multidisciplinary,Mathematics
Journal title
BIOMETRIKA
ISSN journal
00063444 → ACNP
Volume
87
Issue
3
Year of publication
2000
Pages
675 - 687
Database
ISI
SICI code
0006-3444(200009)87:3<675:BPOTRE>2.0.ZU;2-R
Abstract
To bound the influence of a leverage point, generalised M-estimators have b een suggested. However, the usual generalised M-estimator of regression has a breakdown point that is less than the inverse of its dimension. This pap er shows that dimension-independent positive breakdown points can be attain ed by a class of well-defined generalised M-estimators with redescending sc ores. The solution can be determined through optimisation of t-type likelih ood applied to properly weighted residuals. The highest breakdown point of 1/2 is attained by Cauchy score. these bounded-influence and high-breakdown estimators can be viewed as a fully iterated version of the one-step gener alised M-estimates of Simpson, Ruppert & Carroll (1992) with the two advant ages of easier interpretability and avoidance of undesirable roots to estim ating equations. Given the design-dependent weights, they can be computed v ia EM algorithms. Empirical investigations show that they are highly compet itive with other robust estimators of regression.