Open Access
June, 1982 Recursive Computation of $M$-Estimates for the Parameters of a Finite Autoregressive Process
Katherine Campbell
Ann. Statist. 10(2): 442-453 (June, 1982). DOI: 10.1214/aos/1176345785


Stochastic approximation methods are used to generate a sequence of "$M$-estimates" for the unknown parameters of an autoregressive process of known, finite order which may have heavy-tailed innovations. Weak dependence properties, which can be demonstrated for many autoregressive processes, are used in the proof that the sequence converges almost surely to the parameters. A brief Monte Carlo study verifies that bounded influence functions provide protection for recursive procedures against heavy-tailed innovations.


Download Citation

Katherine Campbell. "Recursive Computation of $M$-Estimates for the Parameters of a Finite Autoregressive Process." Ann. Statist. 10 (2) 442 - 453, June, 1982.


Published: June, 1982
First available in Project Euclid: 12 April 2007

zbMATH: 0492.62076
MathSciNet: MR653519
Digital Object Identifier: 10.1214/aos/1176345785

Primary: 62L12
Secondary: 62G35 , 62L20 , 62M10

Keywords: robustness , stochastic approximation , Weak dependence

Rights: Copyright © 1982 Institute of Mathematical Statistics

Vol.10 • No. 2 • June, 1982
Back to Top