Robust estimation in finite mixture models

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2021-07-01 DOI:10.1051/ps/2023004

Alexandre Lecestre

引用次数: 1

Abstract

We observe a n-sample, the distribution of which is assumed to belong, or at least to be close enough, to a given mixture model. We propose an estimator of this distribution that belongs to our model and possesses some robustness properties with respect to a possible misspecification of it. We establish a non-asymptotic deviation bound for the Hellinger distance between the target distribution and its estimator when the model consists of a mixture of densities that belong to VC-subgraph classes. Under suitable assumptions and when the mixture model is well-specified, we derive risk bounds for the parameters of the mixture. Finally, we design a statistical procedure that allows us to select from the data the number of components as well as suitable models for each of the densities that are involved in the mixture. These models are chosen among a collection of candidate ones and we show that our selection rule combined with our estimation strategy result in an estimator which satisfies an oracle-type inequality.

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有限混合模型的鲁棒估计

我们观察到一个n样本，它的分布被假设属于，或者至少是足够接近，一个给定的混合模型。我们提出了这个分布的一个估计量，它属于我们的模型，并且对于可能的错误说明具有一些鲁棒性。当模型由属于vc子图类的混合密度组成时，我们建立了目标分布与其估计量之间的海灵格距离的非渐近偏差界。在适当的假设条件下，当混合模型被很好地指定时，我们导出了混合模型参数的风险界。最后，我们设计了一个统计程序，使我们能够从数据中选择组件的数量以及适合混合物中涉及的每个密度的模型。这些模型是从一组候选模型中选择出来的，我们证明了我们的选择规则与我们的估计策略相结合会产生一个满足oracle型不等式的估计器。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Esaim-Probability and Statistics STATISTICS & PROBABILITY-

CiteScore

1.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The journal publishes original research and survey papers in the area of Probability and Statistics. It covers theoretical and practical aspects, in any field of these domains. Of particular interest are methodological developments with application in other scientific areas, for example Biology and Genetics, Information Theory, Finance, Bioinformatics, Random structures and Random graphs, Econometrics, Physics. Long papers are very welcome. Indeed, we intend to develop the journal in the direction of applications and to open it to various fields where random mathematical modelling is important. In particular we will call (survey) papers in these areas, in order to make the random community aware of important problems of both theoretical and practical interest. We all know that many recent fascinating developments in Probability and Statistics are coming from "the outside" and we think that ESAIM: P&S should be a good entry point for such exchanges. Of course this does not mean that the journal will be only devoted to practical aspects.