Artikel
Maximum Likelihood estimation under two-stage adaptive designs with finite first-stage samples
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Autoren
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Caterina May
- Università del Piemonte Orientale, Novara, Italy
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Nancy Flournoy
- University of MIssouri-Columbia, Bellingham, United States
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Chiara Tommasi
- Università degli Studi di Milano, Milano, Italy
| Veröffentlicht: | 26. Februar 2021 |
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Gliederung
Text
In this work, we study the properties of the maximum likelihood estimator (MLE) for the vector parameter of a non-linear model with Gaussian errors. To estimate the multidimensional parameter as precisely as possible, the experimental conditions are chosen according to a two-stage design. The observations are dependent since the second stage design follows an optimality criterion determined by the responses observed at the first stage. The MLE maximizes the whole data likelihood.
Differently from the classical literature, the first stage sample size is assumed to be finite, and hence asymptotic approximation is used only in the second stage. This assumption should improve the standard asymptotic approximation, especially for small or moderate sample size dimensions at the first stage.
We have that the consistency of the MLE maintains and we obtain its asymptotic distribution, which is a specific Gaussian mixture. The results are based on stable convergence.
We perform simulation studies in the case of some specific models.
The authors declare that they have no competing interests.
The authors declare that an ethics committee vote is not required.
References
- 1.
- Flournoy N, May C, Tommasi C. The effects of adaptation on maximum likelihood inference for non-linear models with normal errors. ArXiv. 2019. arXiv:1812.03970
