{"title":"在幂绝对误差损失(PAEL)下的指数分布中均值的最小风险点估计(MRPE)，这是由于估计加上采样成本造成的","authors":"N. Mukhopadhyay, Ya. G. Khariton","doi":"10.1080/07474946.2020.1766930","DOIUrl":null,"url":null,"abstract":"Abstract We begin with a review of asymptotic properties of a purely sequential minimum risk point estimation (MRPE) methodology for an unknown mean in a one-parameter exponential distribution under a class of generalized loss functions. This class of powered absolute error loss (PAEL) includes both squared error loss (SEL) and absolute error loss (AEL) plus cost of sampling. We prove the asymptotic second-order efficiency property and asymptotic first-order risk efficiency property associated with the purely sequential MRPE problem. For operational convenience, we then move to implement an accelerated sequential MRPE methodology and prove the analogous asymptotic second-order efficiency property and asymptotic first-order risk efficiency property. We follow up with extensive data analysis from simulations and provide illustrations using cancer data.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2020-04-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2020.1766930","citationCount":"8","resultStr":"{\"title\":\"Minimum risk point estimation (MRPE) of the mean in an exponential distribution under powered absolute error loss (PAEL) due to estimation plus cost of sampling\",\"authors\":\"N. Mukhopadhyay, Ya. G. Khariton\",\"doi\":\"10.1080/07474946.2020.1766930\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We begin with a review of asymptotic properties of a purely sequential minimum risk point estimation (MRPE) methodology for an unknown mean in a one-parameter exponential distribution under a class of generalized loss functions. This class of powered absolute error loss (PAEL) includes both squared error loss (SEL) and absolute error loss (AEL) plus cost of sampling. We prove the asymptotic second-order efficiency property and asymptotic first-order risk efficiency property associated with the purely sequential MRPE problem. For operational convenience, we then move to implement an accelerated sequential MRPE methodology and prove the analogous asymptotic second-order efficiency property and asymptotic first-order risk efficiency property. We follow up with extensive data analysis from simulations and provide illustrations using cancer data.\",\"PeriodicalId\":48879,\"journal\":{\"name\":\"Sequential Analysis-Design Methods and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2020-04-02\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"https://sci-hub-pdf.com/10.1080/07474946.2020.1766930\",\"citationCount\":\"8\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Sequential Analysis-Design Methods and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/07474946.2020.1766930\",\"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":"Sequential Analysis-Design Methods and Applications","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1080/07474946.2020.1766930","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
Minimum risk point estimation (MRPE) of the mean in an exponential distribution under powered absolute error loss (PAEL) due to estimation plus cost of sampling
Abstract We begin with a review of asymptotic properties of a purely sequential minimum risk point estimation (MRPE) methodology for an unknown mean in a one-parameter exponential distribution under a class of generalized loss functions. This class of powered absolute error loss (PAEL) includes both squared error loss (SEL) and absolute error loss (AEL) plus cost of sampling. We prove the asymptotic second-order efficiency property and asymptotic first-order risk efficiency property associated with the purely sequential MRPE problem. For operational convenience, we then move to implement an accelerated sequential MRPE methodology and prove the analogous asymptotic second-order efficiency property and asymptotic first-order risk efficiency property. We follow up with extensive data analysis from simulations and provide illustrations using cancer data.
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The purpose of Sequential Analysis is to contribute to theoretical and applied aspects of sequential methodologies in all areas of statistical science. Published papers highlight the development of new and important sequential approaches.
Interdisciplinary articles that emphasize the methodology of practical value to applied researchers and statistical consultants are highly encouraged. Papers that cover contemporary areas of applications including animal abundance, bioequivalence, communication science, computer simulations, data mining, directional data, disease mapping, environmental sampling, genome, imaging, microarrays, networking, parallel processing, pest management, sonar detection, spatial statistics, tracking, and engineering are deemed especially important. Of particular value are expository review articles that critically synthesize broad-based statistical issues. Papers on case-studies are also considered. All papers are refereed.
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