Open Access
June 1996 Adaptive estimation in a random coefficient autoregressive model
Hira L. Koul, Anton Schick
Ann. Statist. 24(3): 1025-1052 (June 1996). DOI: 10.1214/aos/1032526954


This paper proves the local asymptotic normality of a stationary and ergodic first order random coefficient autoregressive model in a semiparametric setting. This result is used to show that Stein's necessary condition for adaptive estimation of the mean of the random coefficient is satisfied if the distributions of the innovations and the errors in the random coefficients are symmetric around zero. Under these symmetry assumptions, a locally asymptotically minimax adaptive estimator of the mean of the random coefficient is constructed. The paper also proves the asymptotic normality of generalized M-estimators of the parameter of interest. These estimators are used as preliminary estimators in the above construction.


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Hira L. Koul. Anton Schick. "Adaptive estimation in a random coefficient autoregressive model." Ann. Statist. 24 (3) 1025 - 1052, June 1996.


Published: June 1996
First available in Project Euclid: 20 September 2002

zbMATH: 0906.62087
MathSciNet: MR1401835
Digital Object Identifier: 10.1214/aos/1032526954

Primary: 62G05 , 62M10

Keywords: Ergodic , generalized $M$-estimator , Locally asymptotically minimax adaptive , semiparametric , stationary

Rights: Copyright © 1996 Institute of Mathematical Statistics

Vol.24 • No. 3 • June 1996
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