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Koul, Hira L.; Schick, Anton

Adaptive estimation in a random coefficient autoregressive model. (English) Zbl 0906.62087

Ann. Stat. 24, No. 3, 1025-1052 (1996).
Summary: 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 C. Stein’s [Proc. 3rd Berkeley Sympos. Math. Statist. Probability 1, 187-195 (1956; Zbl 0074.34801)] 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.

Cited in 28 Documents

MSC:

62M10 Time series, auto-correlation, regression, etc. in statistics (GARCH)
62G05 Nonparametric estimation
62G35 Nonparametric robustness
62G20 Asymptotic properties of nonparametric inference

Keywords:

semiparametric; stationary; ergodic; generalized \(M\)-estimator; local asymptotic normality; LAN; locally asymptotically minimax adaptive estimator

Citations:

Zbl 0074.34801
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Full Text: DOI

References:

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[21] EAST LANSING, MICHIGAN 48824-1027 BINGHAMTON, NEW YORK 13902-6000 E-MAIL: 20974AJT@ibm.msu.edu E-MAIL: anton@math.binghamton.edu
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