季节性马尔可夫调制泊松过程参数的估计

Q Mathematics Statistical Methodology Pub Date : 2015-09-01 DOI:10.1016/j.stamet.2015.04.003

Armelle Guillou , Stéphane Loisel , Gilles Stupfler

{"title":"季节性马尔可夫调制泊松过程参数的估计","authors":"Armelle Guillou , Stéphane Loisel , Gilles Stupfler","doi":"10.1016/j.stamet.2015.04.003","DOIUrl":null,"url":null,"abstract":"<div><p>Motivated by seasonality and regime-switching features of some insurance claim counting processes, we study the statistical analysis of a Markov-modulated Poisson process featuring seasonality. We prove the strong consistency and the asymptotic normality<span> of a maximum split-time likelihood estimator of the parameters of this model, and present an algorithm to compute it in practice. The method is illustrated on a small simulation study and a real data analysis.</span></p></div>","PeriodicalId":48877,"journal":{"name":"Statistical Methodology","volume":"26 ","pages":"Pages 103-123"},"PeriodicalIF":0.0000,"publicationDate":"2015-09-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1016/j.stamet.2015.04.003","citationCount":"8","resultStr":"{\"title\":\"Estimating the parameters of a seasonal Markov-modulated Poisson process\",\"authors\":\"Armelle Guillou , Stéphane Loisel , Gilles Stupfler\",\"doi\":\"10.1016/j.stamet.2015.04.003\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>Motivated by seasonality and regime-switching features of some insurance claim counting processes, we study the statistical analysis of a Markov-modulated Poisson process featuring seasonality. We prove the strong consistency and the asymptotic normality<span> of a maximum split-time likelihood estimator of the parameters of this model, and present an algorithm to compute it in practice. The method is illustrated on a small simulation study and a real data analysis.</span></p></div>\",\"PeriodicalId\":48877,\"journal\":{\"name\":\"Statistical Methodology\",\"volume\":\"26 \",\"pages\":\"Pages 103-123\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2015-09-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1016/j.stamet.2015.04.003\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Statistical Methodology\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1572312715000325\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q\",\"JCRName\":\"Mathematics\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Statistical Methodology","FirstCategoryId":"1085","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1572312715000325","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q","JCRName":"Mathematics","Score":null,"Total":0}

引用次数: 8

摘要

基于保险理赔过程的季节性和制度切换特征，研究了具有季节性特征的马尔可夫调制泊松过程的统计分析。证明了该模型参数的最大分裂时间似然估计量的强相合性和渐近正态性，并给出了一种实际计算算法。通过小型仿真研究和实际数据分析说明了该方法的有效性。

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

微信好友朋友圈 QQ好友复制链接

本刊更多论文

Estimating the parameters of a seasonal Markov-modulated Poisson process

Motivated by seasonality and regime-switching features of some insurance claim counting processes, we study the statistical analysis of a Markov-modulated Poisson process featuring seasonality. We prove the strong consistency and the asymptotic normality of a maximum split-time likelihood estimator of the parameters of this model, and present an algorithm to compute it in practice. The method is illustrated on a small simulation study and a real data analysis.

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

Statistical Methodology STATISTICS & PROBABILITY-

CiteScore

0.59

自引率

0.00%

发文量

期刊介绍： Statistical Methodology aims to publish articles of high quality reflecting the varied facets of contemporary statistical theory as well as of significant applications. In addition to helping to stimulate research, the journal intends to bring about interactions among statisticians and scientists in other disciplines broadly interested in statistical methodology. The journal focuses on traditional areas such as statistical inference, multivariate analysis, design of experiments, sampling theory, regression analysis, re-sampling methods, time series, nonparametric statistics, etc., and also gives special emphasis to established as well as emerging applied areas.