High Breakdown-Point Estimates of Regression by Means of the Minimization of an Efficient Scale.
Abstract
A new class of robust estimates, called tau-estimates, is introduced in this paper. These estimates have simultaneously the following properties: (1) they are qualitatively robust; (2) their breakdown point is 0.5; and (3) they are highly efficient for regression models with normal errors. These estimates are defined by minimizing a new scale estimate, tau, applied to the residuals. Asymptotically, a tau-estimate is equivalent to an M-estimate with a psi-function given by a weighted average of two psi-functions, one corresponding to a very robust estimate and the other to a highly efficient estimate. The weights are adaptive, and depend on the underlying error distribution. We prove consistency and asymptotical normality, and give a convergent iterative computing algorithm. Finally we compare the biases produced by gross error contamination in the tau-estimates and optimal bounded influence estimates. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Nov 30, 1986
- Accession Number
- ADA176220
Entities
People
- Ruben H. Zamar
- Victor J. Yohai
Organizations
- University of Washington