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. © Institute of Mathematical Statistics, 2011.
| Original language | English |
|---|---|
| Pages (from-to) | 1526-1550 |
| Journal | Annals of Statistics |
| Volume | 39 |
| Issue number | 3 |
| DOIs | |
| Publication status | Published - Jun 2011 |
| Externally published | Yes |
Bibliographical note
Publication details (e.g. title, author(s), publication statuses and dates) are captured on an “AS IS” and “AS AVAILABLE” basis at the time of record harvesting from the data source. Suggestions for further amendments or supplementary information can be sent to [email protected].Research Keywords
- Fisher's information matrix
- Least squares estimates
- Mean squared prediction errors
- Stochastic regression models
- Uniform moment bounds