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March, 1987 On Adaptive Estimation in Stationary ARMA Processes
Jens-Peter Kreiss
Ann. Statist. 15(1): 112-133 (March, 1987). DOI: 10.1214/aos/1176350256

Abstract

We consider the estimation problem for the parameter $\vartheta_0$ of a stationary ARMA $(p, q)$ process, with independent and identically, but not necessary normally distributed errors. First we prove local asymptotic normality (LAN) for this model. Then we construct locally asymptotically minimax (LAM) estimators, which asymptotically achieve the smallest possible covariance matrix. Utilizing these, we finally obtain strongly adaptive estimators, by using usual kernel estimators for the score function $\dot{\varphi} = -f'/2 f$, where $f$ denotes the density of the error distribution. These estimates turn out to be asymptotically optimal in the LAM sense for a wide class of symmetric densities $f$.

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Jens-Peter Kreiss. "On Adaptive Estimation in Stationary ARMA Processes." Ann. Statist. 15 (1) 112 - 133, March, 1987. https://doi.org/10.1214/aos/1176350256

Information

Published: March, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0616.62042
MathSciNet: MR885727
Digital Object Identifier: 10.1214/aos/1176350256

Subjects:
Primary: 62F35
Secondary: 62E20, 62F12, 62M09

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 1 • March, 1987
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