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.
"Uniform moment bounds of Fisher’s information with applications to time series." Ann. Statist. 39 (3) 1526 - 1550, June 2011. https://doi.org/10.1214/10-AOS861