Moderate deviations of minimum contrast estimators under contamination
Moderate deviations of minimum contrast estimators under contamination
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DOI：
10.1214/aos/1056562465
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发表时间：
2003-06
影响因子：
4.5
通讯作者：
T. Inglot;W. Kallenberg
中科院分区：
文献类型：
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作者：
T. Inglot;W. Kallenberg
由于统计模型是对现实的简化，因此在估计理论中研究估计量在与所提出的模型（略微）不同的分布下的行为是很重要的。在检验理论中，当处理估计了干扰参数的检验统计量时，需要了解干扰参数的估计量在替代方案下的行为以评估功效。本文研究了最小对比度估计的中偏差行为，不仅在假设模型下，而且在接近模型的分布下。一个特定的例子是（多变量）最大似然估计所提出的模型内确定。设置是相当普遍的，例如也包括离散分布。当将最小对比度估计与参数空间中的"自然"参数进行比较时，以及当将其与参数空间中的建议"真"值进行比较时，确定备选方案下的收敛速率。结果表明，在该模型下，极大似然估计在局部意义下的渐近最优性在中等偏差区域内继续保持。
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. The rate of convergence under alternatives is determined both when comparing the minimum contrast estimator with a "natural" parameter in the parameter space and when comparing it with the proposed "true" value in the parameter space. It turns out that under the model the asymptotic optimality of the maximum likelihood estimator in the local sense continues to hold in the moderate deviation area.