Uniform moment bounds of Fisher's information with applications to time series

Abstract

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.

arXiv commentPublished in at http://dx.doi.org/10.1214/10-AOS861 the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)

References in corpus (3)

• Order selection for same-realization predictions in autoregressive processes
• Uniform moment bounds of Fisher's information with applications to time series
• On prediction errors in regression models with nonstationary regressors

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