### Abstract

Since statistical models are simplifications of reality, it is important in estimation theory to study the behavior of estimators also under distributions (slightly) different from the proposed model. In testing theory, when dealing with test statistics where nuisance parameters are estimated, knowledge of the behavior of the estimators of the nuisance parameters is needed under alternatives to evaluate the power. In this paper the moderate deviation behavior of the (multivariate) maximum likelihood estimator determined within a proposed model is investigated not only under this model, but also under distributions close to the model. The set-up is quite general, including for instance also discrete distributions.

Original language | Undefined |
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Place of Publication | Enschede |

Publisher | University of Twente, Department of Applied Mathematics |

Publication status | Published - 2000 |

### Publication series

Name | |
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Publisher | Department of Applied Mathematics, University of Twente |

No. | 1519 |

ISSN (Print) | 0169-2690 |

### Keywords

- IR-65707
- MSC-62H12
- EWI-3339
- MSC-60F10
- MSC-62F12
- MSC-62E20

## Cite this

Inglot, T., & Kallenberg, W. C. M. (2000).

*Moderate deviations of maximum likelihood estimators under alternatives*. Enschede: University of Twente, Department of Applied Mathematics.