### 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 minimum contrast estimators is investigated not only under the supposed model, but also under distributions close to the model. A particular example is the (multivariate) maximum likelihood estimator determined within the proposed model. The set-up is quite general, including for instance also discrete distributions.

Original language | English |
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Place of Publication | Enschede |

Publisher | University of Twente, Faculty of Mathematical Sciences |

Number of pages | 31 |

Publication status | Published - 2001 |

### Publication series

Name | Memorandum / Department of Applied Mathematics |
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Publisher | University of Twente, Faculty of Mathematical Sciences |

No. | 1598 |

ISSN (Print) | 0169-2690 |

### Keywords

- MSC-60F10
- MSC-62H12
- EWI-3418
- MSC-62F12
- IR-65785
- MSC-62E20

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## Cite this

Inglot, T., & Kallenberg, W. C. M. (2001).

*Moderate deviations of minimum contrast estimators under contamination*. (Memorandum / Department of Applied Mathematics; No. 1598). Enschede: University of Twente, Faculty of Mathematical Sciences.