通过平均边际似然来量化与一组随机曲线的接近程度

IF 0.6 4区数学 Q4 STATISTICS & PROBABILITY

Esaim-Probability and Statistics Pub Date : 2020-12-15 DOI:10.1051/PS/2020028

C'edric Rommel, J. Frédéric Bonnans, Baptiste Gregorutti, P. Martinon

{"title":"通过平均边际似然来量化与一组随机曲线的接近程度","authors":"C'edric Rommel, J. Frédéric Bonnans, Baptiste Gregorutti, P. Martinon","doi":"10.1051/PS/2020028","DOIUrl":null,"url":null,"abstract":"In this paper, we tackle the problem of quantifying the closeness of a newly observed curve to a given sample of random functions, supposed to have been sampled from the same distribution. We define a probabilistic criterion for such a purpose, based on the marginal density functions of an underlying random process. For practical applications, a class of estimators based on the aggregation of multivariate density estimators is introduced and proved to be consistent. We illustrate the effectiveness of our estimators, as well as the practical usefulness of the proposed criterion, by applying our method to a dataset of real aircraft trajectories.","PeriodicalId":51249,"journal":{"name":"Esaim-Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2020-12-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"Quantifying the closeness to a set of random curves via the mean marginal likelihood\",\"authors\":\"C'edric Rommel, J. Frédéric Bonnans, Baptiste Gregorutti, P. Martinon\",\"doi\":\"10.1051/PS/2020028\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"In this paper, we tackle the problem of quantifying the closeness of a newly observed curve to a given sample of random functions, supposed to have been sampled from the same distribution. We define a probabilistic criterion for such a purpose, based on the marginal density functions of an underlying random process. For practical applications, a class of estimators based on the aggregation of multivariate density estimators is introduced and proved to be consistent. We illustrate the effectiveness of our estimators, as well as the practical usefulness of the proposed criterion, by applying our method to a dataset of real aircraft trajectories.\",\"PeriodicalId\":51249,\"journal\":{\"name\":\"Esaim-Probability and Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2020-12-15\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Esaim-Probability and Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1051/PS/2020028\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"STATISTICS & PROBABILITY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Esaim-Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1051/PS/2020028","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}

引用次数: 2

摘要

在本文中，我们解决了量化新观察曲线与给定随机函数样本的接近程度的问题，假设这些随机函数样本来自同一分布。基于底层随机过程的边际密度函数，我们为此目的定义了一个概率准则。在实际应用中，引入了一类基于多元密度估计集合的估计量，并证明了其一致性。通过将我们的方法应用于真实飞机轨迹的数据集，我们说明了我们估计器的有效性，以及所提出标准的实际用途。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Quantifying the closeness to a set of random curves via the mean marginal likelihood

In this paper, we tackle the problem of quantifying the closeness of a newly observed curve to a given sample of random functions, supposed to have been sampled from the same distribution. We define a probabilistic criterion for such a purpose, based on the marginal density functions of an underlying random process. For practical applications, a class of estimators based on the aggregation of multivariate density estimators is introduced and proved to be consistent. We illustrate the effectiveness of our estimators, as well as the practical usefulness of the proposed criterion, by applying our method to a dataset of real aircraft trajectories.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.