Elhadji Ousseynouu Accrachi, Cherif Ahmat Tidiane Aidara, A. S. Dabye
{"title":"关于聚合泊松观测的参数估计","authors":"Elhadji Ousseynouu Accrachi, Cherif Ahmat Tidiane Aidara, A. S. Dabye","doi":"10.52737/18291163-2019.11.5-1-13","DOIUrl":null,"url":null,"abstract":"We consider the problem of parameter estimation by the observations of inhomogeneous Poisson processes. The intensity function of the process is supposed to be a smooth function with respect to the unknown parameter. We propose a Chi-square statistic on the base of agregated observations and we define a Minimum Chi-square Estimator with the help of this statistics. We show this that estimator is consistent and asymptotically normal. We discuss possible generalizations of the obtained results.","PeriodicalId":42323,"journal":{"name":"Armenian Journal of Mathematics","volume":null,"pages":null},"PeriodicalIF":0.5000,"publicationDate":"2019-04-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"On Parameter Estimation by Aggregated Poisson Observations\",\"authors\":\"Elhadji Ousseynouu Accrachi, Cherif Ahmat Tidiane Aidara, A. S. Dabye\",\"doi\":\"10.52737/18291163-2019.11.5-1-13\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider the problem of parameter estimation by the observations of inhomogeneous Poisson processes. The intensity function of the process is supposed to be a smooth function with respect to the unknown parameter. We propose a Chi-square statistic on the base of agregated observations and we define a Minimum Chi-square Estimator with the help of this statistics. We show this that estimator is consistent and asymptotically normal. We discuss possible generalizations of the obtained results.\",\"PeriodicalId\":42323,\"journal\":{\"name\":\"Armenian Journal of Mathematics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.5000,\"publicationDate\":\"2019-04-26\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Armenian Journal of Mathematics\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.52737/18291163-2019.11.5-1-13\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Armenian Journal of Mathematics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.52737/18291163-2019.11.5-1-13","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
On Parameter Estimation by Aggregated Poisson Observations
We consider the problem of parameter estimation by the observations of inhomogeneous Poisson processes. The intensity function of the process is supposed to be a smooth function with respect to the unknown parameter. We propose a Chi-square statistic on the base of agregated observations and we define a Minimum Chi-square Estimator with the help of this statistics. We show this that estimator is consistent and asymptotically normal. We discuss possible generalizations of the obtained results.
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