Pub Date : 2023-09-20DOI: 10.1080/07474946.2023.2242414
R. N. Rattihalli
AbstractFor a given positive number ‘δ′, we consider a sequence of δ− neighborhoods of the independent and identically distributed (i.i.d.) random variables, from a U(0,1) distribution, and “stop as soon as their union contains the interval (0,1).” We call such a union “a cover.” To find the distributions of N(δ), the stopping time random variable, we need the joint distribution of order statistics from a U(0,1) distribution. For each δ>0 and n=1,2,…, we obtain a general expression for P(N(δ)≤n), and for a fixed value of δ, it is the distribution function of N(δ). For a given n, let Δ(n) be the minimum value of δ, so that the union of the n δ− neighborhoods of the first n observations contains the interval (0,1). Because N(δ)≤n if and only if Δ(n)≤δ, the distributions of Δ(n) can be obtained by fixing n in the general expression for P(N(δ)≤n). To describe the impact of δ on the distribution of N(δ) and that of n on Δ(n), we sketch the graphs of distribution functions and the empirical distribution functions.Keywords: Neighborhoodstopping ruleuniform distributionSubject Classification: MSC 2020: 26B1562E15 ACKNOWLEDGMENTThanks to S. B. Patil and S. R. Rattihalli for their computational assistance.DISCLOSUREThe author has no conflicts of interest to report.
摘要对于给定的正数“δ”，我们从U(0,1)分布中考虑独立同分布(i.i.d)随机变量的δ -邻域序列，并且“当它们的并集包含区间(0,1)时就停止”。我们称这样的联盟为“掩护”。为了求出停止时间随机变量N(δ)的分布，我们需要U(0,1)分布的阶统计量的联合分布。对于每个δ>0且n=1,2，…，我们得到了P(n (δ)≤n)的一般表达式，对于固定值的δ，它是n (δ)的分布函数。对于给定的n，设Δ(n)为Δ的最小值，使得前n个观测值的n个Δ−邻域的并集包含区间(0,1)。因为N(δ)≤N当且仅当Δ(N)≤δ，所以将N固定在P(N(δ)≤N)的一般表达式中，即可得到Δ(N)的分布。为了描述δ对N(δ)和N对Δ(N)分布的影响，我们绘制了分布函数图和经验分布函数图。关键词:邻域停止规则均匀分布主题分类:MSC 2020: 26B1562E15感谢S. B. Patil和S. R. Rattihalli的计算协助。作者无利益冲突需要报告。
{"title":"Distribution of number of observations required to obtain a cover for the support of a uniform distribution","authors":"R. N. Rattihalli","doi":"10.1080/07474946.2023.2242414","DOIUrl":"https://doi.org/10.1080/07474946.2023.2242414","url":null,"abstract":"AbstractFor a given positive number ‘δ′, we consider a sequence of δ− neighborhoods of the independent and identically distributed (i.i.d.) random variables, from a U(0,1) distribution, and “stop as soon as their union contains the interval (0,1).” We call such a union “a cover.” To find the distributions of N(δ), the stopping time random variable, we need the joint distribution of order statistics from a U(0,1) distribution. For each δ>0 and n=1,2,…, we obtain a general expression for P(N(δ)≤n), and for a fixed value of δ, it is the distribution function of N(δ). For a given n, let Δ(n) be the minimum value of δ, so that the union of the n δ− neighborhoods of the first n observations contains the interval (0,1). Because N(δ)≤n if and only if Δ(n)≤δ, the distributions of Δ(n) can be obtained by fixing n in the general expression for P(N(δ)≤n). To describe the impact of δ on the distribution of N(δ) and that of n on Δ(n), we sketch the graphs of distribution functions and the empirical distribution functions.Keywords: Neighborhoodstopping ruleuniform distributionSubject Classification: MSC 2020: 26B1562E15 ACKNOWLEDGMENTThanks to S. B. Patil and S. R. Rattihalli for their computational assistance.DISCLOSUREThe author has no conflicts of interest to report.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.0,"publicationDate":"2023-09-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136264741","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-09-04DOI: 10.1080/07474946.2023.2224401
S. Dutta, Farha Sultana, S. Kayal
{"title":"Bayesian and non-Bayesian inference for a general family of distributions based on simple step-stress life test using TRV model under type II censoring","authors":"S. Dutta, Farha Sultana, S. Kayal","doi":"10.1080/07474946.2023.2224401","DOIUrl":"https://doi.org/10.1080/07474946.2023.2224401","url":null,"abstract":"","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45885180","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-03DOI: 10.1080/07474946.2023.2204888
Murat Sagir
Abstract This paper deals with testing traffic intensity, which is the most important parameter of the queue system. The Wald-type sequential probability ratio test (SPRT) is performed to determine traffic intensity by taking advantage of the fact that the total number of customers arriving up to the kth service period, including the kth service period, has a negative binomial distribution. Acceptance and rejection limits obtained from the SPRT are arranged as a multiple sampling plan. This plan is applied with a finite Markov chain. Then, the Operating Characteristic (OC) function and the Average Sample Number (ASN) are obtained precisely. Obtaining the standard errors of the sample number compared to the studies on SPRT applications is the novelty brought by this paper. The sequential analysis method based on the finite Markov chain is also applied to a numerical sample.
{"title":"A Sequential Test of Traffic Intensity for the M/M/1 Queueing System","authors":"Murat Sagir","doi":"10.1080/07474946.2023.2204888","DOIUrl":"https://doi.org/10.1080/07474946.2023.2204888","url":null,"abstract":"Abstract This paper deals with testing traffic intensity, which is the most important parameter of the queue system. The Wald-type sequential probability ratio test (SPRT) is performed to determine traffic intensity by taking advantage of the fact that the total number of customers arriving up to the kth service period, including the kth service period, has a negative binomial distribution. Acceptance and rejection limits obtained from the SPRT are arranged as a multiple sampling plan. This plan is applied with a finite Markov chain. Then, the Operating Characteristic (OC) function and the Average Sample Number (ASN) are obtained precisely. Obtaining the standard errors of the sample number compared to the studies on SPRT applications is the novelty brought by this paper. The sequential analysis method based on the finite Markov chain is also applied to a numerical sample.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47341676","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-03DOI: 10.1080/07474946.2023.2201607
E. Mahmoudi, Zahra Nemati, Ashkan Khalifeh
Abstract We consider the problem of bounded risk point estimation for the linear combination of the form where and are the location and scale parameters of a exponential distribution and and are constant. We aim to estimate under the modified squared error loss function using the constraint that the risk per unit cost is bounded above with fixed preassigned, . The two-stage sequential sampling is proposed for estimating The performances of the proposed methodologies are investigated with the help of simulations. Finally, using an actual dataset, the procedure is clearly illustrated.
{"title":"Two-stage estimation of the combination of location and scale parameter of the exponential distribution under the constraint of bounded risk per unit cost index","authors":"E. Mahmoudi, Zahra Nemati, Ashkan Khalifeh","doi":"10.1080/07474946.2023.2201607","DOIUrl":"https://doi.org/10.1080/07474946.2023.2201607","url":null,"abstract":"Abstract We consider the problem of bounded risk point estimation for the linear combination of the form where and are the location and scale parameters of a exponential distribution and and are constant. We aim to estimate under the modified squared error loss function using the constraint that the risk per unit cost is bounded above with fixed preassigned, . The two-stage sequential sampling is proposed for estimating The performances of the proposed methodologies are investigated with the help of simulations. Finally, using an actual dataset, the procedure is clearly illustrated.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"43033764","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-03DOI: 10.1080/07474946.2023.2193612
Francis Bilson Darku, Dorcas Ofori-Boateng, Bhargab Chattopadhyay
Abstract The comparison of Gini inequality indices is an important study related to regional imbalance in equality. In the design of such a study, both the cost constraints and variability of the difference of inequality indices play an active role. In this article, we compare the Gini inequality indices for two regions under cost constraints leveraging on the concept of sequential analysis. Without prior knowledge of the statistical distributions of the data in the two regions of interest, the optimal sample sizes that balance the cost constraint and the accuracy of the comparison cannot be calculated under a fixed-sample-size methodology. Therefore, in this article, we develop a sequential procedure for comparing Gini indices for two regions under a budget constraint. With no specific assumption about the population distribution of the data, we examine and prove the large-sample properties offered by the proposed purely sequential procedure. Further, we use extensive simulations to empirically examine the characteristics of this procedure and illustrate its application using data on the Paycheck Protection Program loan from the U.S. Small Business Administration for the states of Connecticut and Rhode Island.
{"title":"Comparison of Gini indices using sequential approach: Application to the U.S. Small Business Administration data","authors":"Francis Bilson Darku, Dorcas Ofori-Boateng, Bhargab Chattopadhyay","doi":"10.1080/07474946.2023.2193612","DOIUrl":"https://doi.org/10.1080/07474946.2023.2193612","url":null,"abstract":"Abstract The comparison of Gini inequality indices is an important study related to regional imbalance in equality. In the design of such a study, both the cost constraints and variability of the difference of inequality indices play an active role. In this article, we compare the Gini inequality indices for two regions under cost constraints leveraging on the concept of sequential analysis. Without prior knowledge of the statistical distributions of the data in the two regions of interest, the optimal sample sizes that balance the cost constraint and the accuracy of the comparison cannot be calculated under a fixed-sample-size methodology. Therefore, in this article, we develop a sequential procedure for comparing Gini indices for two regions under a budget constraint. With no specific assumption about the population distribution of the data, we examine and prove the large-sample properties offered by the proposed purely sequential procedure. Further, we use extensive simulations to empirically examine the characteristics of this procedure and illustrate its application using data on the Paycheck Protection Program loan from the U.S. Small Business Administration for the states of Connecticut and Rhode Island.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44226070","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-07-03DOI: 10.1080/07474946.2023.2221996
Manuel Cabral Morais, P. Wittenberg, S. Knoth
Abstract Geometrically distributed counts arise in the industry. Ideally, they should be monitored using a control chart whose average run length (ARL) function achieves a maximum when the process is in control; that is, the chart is ARL-unbiased. Moreover, its in-control ARL should coincide with a reasonably large and prespecified value. Because dependence among successive geometric counts is occasionally a more sensible assumption than independence, we assess the impact of using an ARL-unbiased chart specifically designed for monitoring independent geometric counts when, in fact, these counts are autocorrelated. We derive an ARL-unbiased modified chart for monitoring geometric first-order integer-valued autoregressive or GINAR(1) counts. We provide compelling illustrations of this chart and discuss its use to monitor other autoregressive counts with a geometric marginal distribution.
{"title":"An ARL-unbiased modified chart for monitoring autoregressive counts with geometric marginal distributions","authors":"Manuel Cabral Morais, P. Wittenberg, S. Knoth","doi":"10.1080/07474946.2023.2221996","DOIUrl":"https://doi.org/10.1080/07474946.2023.2221996","url":null,"abstract":"Abstract Geometrically distributed counts arise in the industry. Ideally, they should be monitored using a control chart whose average run length (ARL) function achieves a maximum when the process is in control; that is, the chart is ARL-unbiased. Moreover, its in-control ARL should coincide with a reasonably large and prespecified value. Because dependence among successive geometric counts is occasionally a more sensible assumption than independence, we assess the impact of using an ARL-unbiased chart specifically designed for monitoring independent geometric counts when, in fact, these counts are autocorrelated. We derive an ARL-unbiased modified chart for monitoring geometric first-order integer-valued autoregressive or GINAR(1) counts. We provide compelling illustrations of this chart and discuss its use to monitor other autoregressive counts with a geometric marginal distribution.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47081190","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-03DOI: 10.1080/07474946.2023.2187416
Chao Gu, Suthakaran Ratnasingam
Abstract We propose a novel sequential change point detection method in linear models. Our method uses a given historical data set to determine the prechange model. Significant features are selected using the ranking procedure, which is an innovative approach aimed at revealing the rank of all features in terms of their effects on the model. We establish the asymptotic properties of the test statistic under the null and alternative hypotheses. Simulations are conducted to illustrate the performance of the proposed method. We conclude with a real data application to illustrate the detection procedure.
{"title":"Real-time change point detection in linear models using the ranking selection procedure","authors":"Chao Gu, Suthakaran Ratnasingam","doi":"10.1080/07474946.2023.2187416","DOIUrl":"https://doi.org/10.1080/07474946.2023.2187416","url":null,"abstract":"Abstract We propose a novel sequential change point detection method in linear models. Our method uses a given historical data set to determine the prechange model. Significant features are selected using the ranking procedure, which is an innovative approach aimed at revealing the rank of all features in terms of their effects on the model. We establish the asymptotic properties of the test statistic under the null and alternative hypotheses. Simulations are conducted to illustrate the performance of the proposed method. We conclude with a real data application to illustrate the detection procedure.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42962930","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-03DOI: 10.1080/07474946.2023.2184831
Wenyu Liu, D. Coad
Abstract Several experimental treatments are often compared with a common control in a clinical trial nowadays. A group-sequential design incorporating response-adaptive randomization can help to increase the probability of receiving a more promising treatment for patients in the trial and to detect a treatment effect early so as to benefit the whole population of interest. With such ethical advantages, the trial design has invoked investigation using the Bayesian approach. In the frequentist approach, the type I error rate of a multi-armed trial may involve two error elements, the inflated error rates caused by multiple treatment comparisons and sequential testing. In this study, a group-sequential global test was considered. By monitoring the response-adaptive design at a continuous information time, calculation of the information time and two optimal response-adaptive sampling rules for multi-armed trials were described. Operating characteristics of the designs were investigated via simulation for censored exponential survival outcomes and using patient data sampled from a four-armed binary trial to demonstrate their practical applicability. Our results showed that, in general, the adaptive designs preserved ethical advantages in terms of reducing the average numbers of patients and failures compared with a group-sequential non-adaptive randomized design, while not adversely affecting the power.
{"title":"Group-sequential response-adaptive designs for multi-armed trials","authors":"Wenyu Liu, D. Coad","doi":"10.1080/07474946.2023.2184831","DOIUrl":"https://doi.org/10.1080/07474946.2023.2184831","url":null,"abstract":"Abstract Several experimental treatments are often compared with a common control in a clinical trial nowadays. A group-sequential design incorporating response-adaptive randomization can help to increase the probability of receiving a more promising treatment for patients in the trial and to detect a treatment effect early so as to benefit the whole population of interest. With such ethical advantages, the trial design has invoked investigation using the Bayesian approach. In the frequentist approach, the type I error rate of a multi-armed trial may involve two error elements, the inflated error rates caused by multiple treatment comparisons and sequential testing. In this study, a group-sequential global test was considered. By monitoring the response-adaptive design at a continuous information time, calculation of the information time and two optimal response-adaptive sampling rules for multi-armed trials were described. Operating characteristics of the designs were investigated via simulation for censored exponential survival outcomes and using patient data sampled from a four-armed binary trial to demonstrate their practical applicability. Our results showed that, in general, the adaptive designs preserved ethical advantages in terms of reducing the average numbers of patients and failures compared with a group-sequential non-adaptive randomized design, while not adversely affecting the power.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48620301","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-03DOI: 10.1080/07474946.2023.2193593
C. Makasu
Abstract We prove a one-sided maximal inequality for a randomly stopped Bessel process of dimension For the special case when α = 1, we obtain a sharp Burkholder-Gundy inequality for Brownian motion as a consequence. An application of the present results is also given.
{"title":"One-sided maximal inequalities for a randomly stopped Bessel process","authors":"C. Makasu","doi":"10.1080/07474946.2023.2193593","DOIUrl":"https://doi.org/10.1080/07474946.2023.2193593","url":null,"abstract":"Abstract We prove a one-sided maximal inequality for a randomly stopped Bessel process of dimension For the special case when α = 1, we obtain a sharp Burkholder-Gundy inequality for Brownian motion as a consequence. An application of the present results is also given.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46311055","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2023-04-03DOI: 10.1080/07474946.2023.2193602
A. Novikov, Andrei Novikov, Fahil Farkhshatov
Abstract In this article, we deal with problems of testing hypotheses in the framework of sequential statistical analysis. The main concern is the optimal design and performance evaluation of sampling plans in Kiefer-Weiss problems. The main goal of the Kiefer-Weiss problem is designing hypothesis tests that minimize the maximum average sample number, over all parameter values, as opposed to both the sequential probability tests (SPRTs) minimizing the average sample number only at two hypothesis points and the classical fixed-sample-size test. For observations that follow a distribution from an exponential family of the continuous type, we provide algorithms for optimal design in the modified Kiefer-Weiss problem and obtain formulas for evaluating the performance of sequential tests by calculating the operating characteristic function, the average sample number, and some related characteristics. These formulas cover, as a particular case, the SPRTs and their truncated versions, as well as optimal finite-horizon sequential tests. In the setting of the original Kiefer-Weiss problem we apply the method of our recent work (Sequential Analysis 2022, 41(2), 198–219) for numerical construction of the optimal tests. For the particular case of sampling from a normal distribution with a known variance, we make numerical comparisons of the Kiefer-Weiss solution with the SPRT and the fixed-sample-size test provided that the three tests have the same levels of the error probabilities. All of the algorithms are implemented in the form of computer code written in the R programming language and are available at the GitHub public repository (https://github.com/tosinabase/Kiefer-Weiss). Guidelines on the adaptation of the program code to other exponential family distributions are provided.
{"title":"Numerical solution of Kiefer-Weiss problems when sampling from continuous exponential families","authors":"A. Novikov, Andrei Novikov, Fahil Farkhshatov","doi":"10.1080/07474946.2023.2193602","DOIUrl":"https://doi.org/10.1080/07474946.2023.2193602","url":null,"abstract":"Abstract In this article, we deal with problems of testing hypotheses in the framework of sequential statistical analysis. The main concern is the optimal design and performance evaluation of sampling plans in Kiefer-Weiss problems. The main goal of the Kiefer-Weiss problem is designing hypothesis tests that minimize the maximum average sample number, over all parameter values, as opposed to both the sequential probability tests (SPRTs) minimizing the average sample number only at two hypothesis points and the classical fixed-sample-size test. For observations that follow a distribution from an exponential family of the continuous type, we provide algorithms for optimal design in the modified Kiefer-Weiss problem and obtain formulas for evaluating the performance of sequential tests by calculating the operating characteristic function, the average sample number, and some related characteristics. These formulas cover, as a particular case, the SPRTs and their truncated versions, as well as optimal finite-horizon sequential tests. In the setting of the original Kiefer-Weiss problem we apply the method of our recent work (Sequential Analysis 2022, 41(2), 198–219) for numerical construction of the optimal tests. For the particular case of sampling from a normal distribution with a known variance, we make numerical comparisons of the Kiefer-Weiss solution with the SPRT and the fixed-sample-size test provided that the three tests have the same levels of the error probabilities. All of the algorithms are implemented in the form of computer code written in the R programming language and are available at the GitHub public repository (https://github.com/tosinabase/Kiefer-Weiss). Guidelines on the adaptation of the program code to other exponential family distributions are provided.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2023-04-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41343230","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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