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On adaptive estimation based on ranks in ARMA processes

Allali J., Kaaouachi A., Melhaoui S.

Probability and Mathematical Statistics

2002

Vol. 22, Fasc. 2

293--302

This paper describes the adaptive estimation problem based on ranks for the parameter of an ARMA process. The local asymptotic normality property with a ranked based central sequence allows for the construction of estimators which are locally asymptotically minimax (LAM). By using a consistent estimate of the score function, we obtain the adaptive estimators which are LAM and which do not depend on the innovation density.