Fisher Consistency of AM-Estimates of the Autoregression Parameter Using Hard Rejection Filter Cleaners
Abstract
An AM estimate phi of the AR(1) parameter phi is a solution of the M-estimate equation sum from 1 to n of x sub(t-1) Ps (Y sub t - phi (x sub(t-1)/S sub t), where x sub t-1, t=0,2, satisfies the robust filter recursion x' sub t = phi (x' sub t-1) + s sub t psi* ( L y sub t) -psi (x' sub t -1)/s sub b) and S sub t is a data dependent scale which satisfies = O an auxiliary recursion. The AM-estimate may be viewed as a special kind of bounded influence regression which provides robustness toward contamination models of the type y sub t = (1 - z sub t) x sub t + z sub t w sub t where z sub t is a 0-1 process, w sub t is a contamination process and x sub t is an AR(1) process with parameter phi. While AM-estimates have considerable heuristic appeal, and cope with time series outliers quite well, they are not in general Fisher consistent. This paper shows that under mild conditions, phi' is Fisher consistent when Psi is of hard-rejection type.
Document Details
- Document Type
- Technical Report
- Publication Date
- Feb 01, 1987
- Accession Number
- ADA198962
Entities
People
- R. D. Martin
- Victor J. Yohai
Organizations
- University of Washington