{"title":"漏报计数的泊松平均值检验","authors":"Debjit Sengupta, Surupa Roy, Tathagata Banerjee","doi":"10.1214/20-bjps493","DOIUrl":null,"url":null,"abstract":"For modelling unbounded count data, Poisson distribution is a natural choice. However, count data arising in various fields of scientific research are often under-reported. In such situations, inference carried out on the basis of Poisson model will result in biased parameter estimates and suboptimal tests. A modified Poisson model is developed to accommodate the possible undercount. For model-identifiability a double sampling scheme of data collection has been adopted. The focus of this paper is to develop asymptotically optimal tests for the Poisson mean in presence of undercount. Simulation study is conducted to compare the performance of the tests with respect to level and power and also to investigate the impact of ignoring undercount on each of the tests. The findings are validated using real life data.","PeriodicalId":51242,"journal":{"name":"Brazilian Journal of Probability and Statistics","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Testing of Poisson mean with under-reported counts\",\"authors\":\"Debjit Sengupta, Surupa Roy, Tathagata Banerjee\",\"doi\":\"10.1214/20-bjps493\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"For modelling unbounded count data, Poisson distribution is a natural choice. However, count data arising in various fields of scientific research are often under-reported. In such situations, inference carried out on the basis of Poisson model will result in biased parameter estimates and suboptimal tests. A modified Poisson model is developed to accommodate the possible undercount. For model-identifiability a double sampling scheme of data collection has been adopted. The focus of this paper is to develop asymptotically optimal tests for the Poisson mean in presence of undercount. Simulation study is conducted to compare the performance of the tests with respect to level and power and also to investigate the impact of ignoring undercount on each of the tests. The findings are validated using real life data.\",\"PeriodicalId\":51242,\"journal\":{\"name\":\"Brazilian Journal of Probability and Statistics\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Brazilian Journal of Probability and Statistics\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1214/20-bjps493\",\"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":"Brazilian Journal of Probability and Statistics","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1214/20-bjps493","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Testing of Poisson mean with under-reported counts
For modelling unbounded count data, Poisson distribution is a natural choice. However, count data arising in various fields of scientific research are often under-reported. In such situations, inference carried out on the basis of Poisson model will result in biased parameter estimates and suboptimal tests. A modified Poisson model is developed to accommodate the possible undercount. For model-identifiability a double sampling scheme of data collection has been adopted. The focus of this paper is to develop asymptotically optimal tests for the Poisson mean in presence of undercount. Simulation study is conducted to compare the performance of the tests with respect to level and power and also to investigate the impact of ignoring undercount on each of the tests. The findings are validated using real life data.
期刊介绍:
The Brazilian Journal of Probability and Statistics aims to publish high quality research papers in applied probability, applied statistics, computational statistics, mathematical statistics, probability theory and stochastic processes.
More specifically, the following types of contributions will be considered:
(i) Original articles dealing with methodological developments, comparison of competing techniques or their computational aspects.
(ii) Original articles developing theoretical results.
(iii) Articles that contain novel applications of existing methodologies to practical problems. For these papers the focus is in the importance and originality of the applied problem, as well as, applications of the best available methodologies to solve it.
(iv) Survey articles containing a thorough coverage of topics of broad interest to probability and statistics. The journal will occasionally publish book reviews, invited papers and essays on the teaching of statistics.