{"title":"从伯努利种群中抽样的Kiefer-Weiss问题的计算方法","authors":"A. Novikov, Andrei Novikov, Fahil Farkhshatov","doi":"10.1080/07474946.2022.2070212","DOIUrl":null,"url":null,"abstract":"Abstract We present a computational approach to the solution of the Kiefer-Weiss problem. Algorithms for construction of the optimal sampling plans and evaluation of their performance are proposed. In the particular case of Bernoulli observations, the proposed algorithms are implemented in the form of R program code. Using the developed computer program, we numerically compare the optimal tests with the respective sequential probability ratio test (SPRT) and the fixed sample size test for a wide range of hypothesized values and type I and type II errors. The results are compared with those of D. Freeman and L. Weiss (Journal of the American Statistical Association, 59, 1964). The R source code for the algorithms of construction of optimal sampling plans and evaluation of their characteristics is available at https://github.com/tosinabase/Kiefer-Weiss.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.6000,"publicationDate":"2021-10-10","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"5","resultStr":"{\"title\":\"A computational approach to the Kiefer-Weiss problem for sampling from a Bernoulli population\",\"authors\":\"A. Novikov, Andrei Novikov, Fahil Farkhshatov\",\"doi\":\"10.1080/07474946.2022.2070212\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Abstract We present a computational approach to the solution of the Kiefer-Weiss problem. Algorithms for construction of the optimal sampling plans and evaluation of their performance are proposed. In the particular case of Bernoulli observations, the proposed algorithms are implemented in the form of R program code. Using the developed computer program, we numerically compare the optimal tests with the respective sequential probability ratio test (SPRT) and the fixed sample size test for a wide range of hypothesized values and type I and type II errors. The results are compared with those of D. Freeman and L. Weiss (Journal of the American Statistical Association, 59, 1964). The R source code for the algorithms of construction of optimal sampling plans and evaluation of their characteristics is available at https://github.com/tosinabase/Kiefer-Weiss.\",\"PeriodicalId\":48879,\"journal\":{\"name\":\"Sequential Analysis-Design Methods and Applications\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2021-10-10\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"5\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Sequential Analysis-Design Methods and Applications\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1080/07474946.2022.2070212\",\"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/10.1080/07474946.2022.2070212","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
A computational approach to the Kiefer-Weiss problem for sampling from a Bernoulli population
Abstract We present a computational approach to the solution of the Kiefer-Weiss problem. Algorithms for construction of the optimal sampling plans and evaluation of their performance are proposed. In the particular case of Bernoulli observations, the proposed algorithms are implemented in the form of R program code. Using the developed computer program, we numerically compare the optimal tests with the respective sequential probability ratio test (SPRT) and the fixed sample size test for a wide range of hypothesized values and type I and type II errors. The results are compared with those of D. Freeman and L. Weiss (Journal of the American Statistical Association, 59, 1964). The R source code for the algorithms of construction of optimal sampling plans and evaluation of their characteristics is available at https://github.com/tosinabase/Kiefer-Weiss.
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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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