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June 2011 Uniform moment bounds of Fisher’s information with applications to time series
Ngai Hang Chan, Ching-Kang Ing
Ann. Statist. 39(3): 1526-1550 (June 2011). DOI: 10.1214/10-AOS861


In this paper, a uniform (over some parameter space) moment bound for the inverse of Fisher’s information matrix is established. This result is then applied to develop moment bounds for the normalized least squares estimate in (nonlinear) stochastic regression models. The usefulness of these results is illustrated using time series models. In particular, an asymptotic expression for the mean squared prediction error of the least squares predictor in autoregressive moving average models is obtained. This asymptotic expression provides a solid theoretical foundation for some model selection criteria.


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Ngai Hang Chan. Ching-Kang Ing. "Uniform moment bounds of Fisher’s information with applications to time series." Ann. Statist. 39 (3) 1526 - 1550, June 2011.


Published: June 2011
First available in Project Euclid: 7 June 2011

zbMATH: 1220.62088
MathSciNet: MR2850211
Digital Object Identifier: 10.1214/10-AOS861

Primary: 62J02
Secondary: 60F25 , 62F12 , 62M10

Keywords: Fisher’s information matrix , least squares estimates , mean squared prediction errors , stochastic regression models , uniform moment bounds

Rights: Copyright © 2011 Institute of Mathematical Statistics


Vol.39 • No. 3 • June 2011
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