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Sequential Analysis-Design Methods and Applications最新文献

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Sequential tracking of an unobservable two-state Markov process under Brownian noise 布朗噪声下不可观测两态马尔可夫过程的顺序跟踪
IF 0.8 4区 数学
Sequential Analysis-Design Methods and Applications Pub Date : 2019-08-03 DOI: 10.1080/07474946.2021.1847924
A. Muravlev, M. Urusov, M. Zhitlukhin
{"title":"Sequential tracking of an unobservable two-state Markov process under Brownian noise","authors":"A. Muravlev, M. Urusov, M. Zhitlukhin","doi":"10.1080/07474946.2021.1847924","DOIUrl":"https://doi.org/10.1080/07474946.2021.1847924","url":null,"abstract":"Abstract We consider an optimal control problem where a Brownian motion with drift is sequentially observed and the sign of the drift coefficient changes at jump times of a symmetric two-state Markov process. The Markov process itself is not observable, and the problem consists of finding a {−1, 1}-valued process that tracks the unobservable process as closely as possible. We present an explicit construction of such a process.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"40 1","pages":"1 - 16"},"PeriodicalIF":0.8,"publicationDate":"2019-08-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2021.1847924","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41414373","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}
引用次数: 1
On the convergence rate of the quasi- to stationary distribution for the Shiryaev-Roberts diffusion 关于Shiryaev-Roberts扩散的拟平稳分布的收敛速度
IF 0.8 4区 数学
Sequential Analysis-Design Methods and Applications Pub Date : 2019-07-05 DOI: 10.1080/07474946.2020.1766926
Kexuan Li, Aleksey S. Polunchenko
{"title":"On the convergence rate of the quasi- to stationary distribution for the Shiryaev-Roberts diffusion","authors":"Kexuan Li, Aleksey S. Polunchenko","doi":"10.1080/07474946.2020.1766926","DOIUrl":"https://doi.org/10.1080/07474946.2020.1766926","url":null,"abstract":"Abstract For the classical Shiryaev-Roberts martingale diffusion considered on the interval where A > 0 is a given absorbing boundary, it is shown that the rate of convergence of the diffusion’s quasi-stationary cumulative distribution function (c.d.f.), to its stationary c.d.f., H(x), as is no worse than uniformly in The result is established explicitly by constructing new tight lower- and upper-bounds for using certain latest monotonicity properties of the modified Bessel K function involved in the exact closed-form formula for recently obtained by Polunchenko (2017b).","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"39 1","pages":"214 - 229"},"PeriodicalIF":0.8,"publicationDate":"2019-07-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2020.1766926","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49452546","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}
引用次数: 2
A hybrid Bayesian-frequentist predictive design for monitoring multi-stage clinical trials 用于监测多阶段临床试验的混合贝叶斯频率预测设计
IF 0.8 4区 数学
Sequential Analysis-Design Methods and Applications Pub Date : 2019-07-03 DOI: 10.1080/07474946.2019.1648919
Z. Djeridi, H. Merabet
{"title":"A hybrid Bayesian-frequentist predictive design for monitoring multi-stage clinical trials","authors":"Z. Djeridi, H. Merabet","doi":"10.1080/07474946.2019.1648919","DOIUrl":"https://doi.org/10.1080/07474946.2019.1648919","url":null,"abstract":"Abstract In this article, we propose a hybrid-Bayesian frequentist approach using a Bayesian sequential prediction of the index of satisfaction. For interim analysis that addresses prediction hypothesis, such as futility monitoring with delayed outcomes, the prediction of satisfaction properly accounts for the amount of data remaining to be observed in a clinical trial and has the flexibility to incorporate additional information via auxiliary variables. The prediction of satisfaction design guarantees the type I error rate and does not require intensive computation or comprehensive simulation. The design is retrospectively applied to a lung cancer clinical trial.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"38 1","pages":"301 - 317"},"PeriodicalIF":0.8,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2019.1648919","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45734394","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}
引用次数: 1
Second-order analysis of regret for sequential estimation of the autoregressive parameter in a first-order autoregressive model 一阶自回归模型中自回归参数序列估计的二阶后悔分析
IF 0.8 4区 数学
Sequential Analysis-Design Methods and Applications Pub Date : 2019-07-03 DOI: 10.1080/07474946.2019.1648933
T. N. Sriram, S. Samadi
{"title":"Second-order analysis of regret for sequential estimation of the autoregressive parameter in a first-order autoregressive model","authors":"T. N. Sriram, S. Samadi","doi":"10.1080/07474946.2019.1648933","DOIUrl":"https://doi.org/10.1080/07474946.2019.1648933","url":null,"abstract":"Abstract This article revisits the problem of sequential point estimation of the autogressive parameter in an autoregressive model of order 1, where the errors are independent and identically distributed with mean 0 and unknown variance . This problem was originally considered in Sriram (1988), where first-order efficiency properties and a second-order expansion for the expected value of a stopping rule were established. Here, we obtain an asymptotic expression for the so-called regret due to not knowing σ, as the cost of estimation error tends to infinity. Under suitable assumptions, our extensive analysis shows that all but one term in the regret are asymptotically bounded. If the errors have a bounded support, however, then the regret remains asymptotically bounded. Finally, we illustrate the performance of our sequential procedure and the associated regret for well-known blowfly data (Nicholson, 1950) and Internet traffic data using the residual bootstrap method for autoregressive models.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"38 1","pages":"411 - 435"},"PeriodicalIF":0.8,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2019.1648933","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49453386","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}
引用次数: 1
Monitoring a Poisson process subject to gradual changes in the arrival rates 监测到达率逐渐变化的泊松过程
IF 0.8 4区 数学
Sequential Analysis-Design Methods and Applications Pub Date : 2019-07-03 DOI: 10.1080/07474946.2019.1648923
Marlo Brown
{"title":"Monitoring a Poisson process subject to gradual changes in the arrival rates","authors":"Marlo Brown","doi":"10.1080/07474946.2019.1648923","DOIUrl":"https://doi.org/10.1080/07474946.2019.1648923","url":null,"abstract":"Abstract We look at a Poisson process where the arrival rates change from a known λ1 to a known λ2. Whereas in most of the literature the change-point is abrupt, we model the more realistic assumption that states that the change happens gradually over a period of time η where η is known. We calculate the probability that the change has started and completed. We also look at optimal stopping rules assuming that there is a cost for a false alarm and a cost per time unit to stop early. We conclude with some numerical results.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"38 1","pages":"358 - 368"},"PeriodicalIF":0.8,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2019.1648923","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45948903","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}
引用次数: 2
A k-stage procedure for estimating the mean vector of a multivariate normal population 估计多元正态总体的平均向量的k阶段程序
IF 0.8 4区 数学
Sequential Analysis-Design Methods and Applications Pub Date : 2019-07-03 DOI: 10.1080/07474946.2019.1648926
Ajit Chaturvedi, Sudeep R. Bapat, Neeraj Joshi
{"title":"A k-stage procedure for estimating the mean vector of a multivariate normal population","authors":"Ajit Chaturvedi, Sudeep R. Bapat, Neeraj Joshi","doi":"10.1080/07474946.2019.1648926","DOIUrl":"https://doi.org/10.1080/07474946.2019.1648926","url":null,"abstract":"Abstract In this article, we have estimated the mean vector of a multivariate normal population by using a k-stage sequential estimation procedure. Point estimation as well as confidence region estimation is done. Second-order approximations are obtained in both the cases. In case of minimum risk point estimation of , negative regret is achieved.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"38 1","pages":"369 - 384"},"PeriodicalIF":0.8,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2019.1648926","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45194257","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}
引用次数: 3
Minimum risk sequential point estimation of the stress-strength reliability parameter for exponential distribution 指数分布下应力-强度可靠性参数的最小风险序贯点估计
IF 0.8 4区 数学
Sequential Analysis-Design Methods and Applications Pub Date : 2019-07-03 DOI: 10.1080/07474946.2019.1649347
E. Mahmoudi, Ashkan Khalifeh, V. Nekoukhou
{"title":"Minimum risk sequential point estimation of the stress-strength reliability parameter for exponential distribution","authors":"E. Mahmoudi, Ashkan Khalifeh, V. Nekoukhou","doi":"10.1080/07474946.2019.1649347","DOIUrl":"https://doi.org/10.1080/07474946.2019.1649347","url":null,"abstract":"Abstract In this article, using purely and two-stage sequential procedures, the problem of minimum risk point estimation of the reliability parameter (R) under the stress–strength model, in case the loss function is squared error plus sampling cost, is considered when the random stress (X) and the random strength (Y) are independent and both have exponential distributions with different scale parameters. The exact distribution of the total sample size and explicit formulas for the expected value and mean squared error of the maximum likelihood estimator of the reliability parameter under the stress–strength model are provided under the two-stage sequential procedure. Using the law of large numbers and Monte Carlo integration, the exact distribution of the stopping rule under the purely sequential procedure is approximated. Moreover, it is shown that both proposed sequential procedures are finite and for special cases the exact distribution of stopping times has a degenerate distribution at the initial sample size. The performances of the proposed methodologies are investigated with the help of simulations. Finally, using a real data set, the procedures are clearly illustrated.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"38 1","pages":"279 - 300"},"PeriodicalIF":0.8,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2019.1649347","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44062906","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}
引用次数: 10
A Khmaladze-transformed test of fit with ML estimation in the presence of recurrent events 在存在重复事件的情况下，用ML估计拟合的khmaladze变换检验
IF 0.8 4区 数学
Sequential Analysis-Design Methods and Applications Pub Date : 2019-07-03 DOI: 10.1080/07474946.2019.1648920
K. Zamba, A. Adekpedjou
{"title":"A Khmaladze-transformed test of fit with ML estimation in the presence of recurrent events","authors":"K. Zamba, A. Adekpedjou","doi":"10.1080/07474946.2019.1648920","DOIUrl":"https://doi.org/10.1080/07474946.2019.1648920","url":null,"abstract":"Abstract This article provides a goodness-of-fit test for the distribution function or the survival function in a recurrent event setting, when the inter-event time parametric structure is estimated from the observed data. Of concern is the null hypothesis that the inter-event time distribution is absolutely continuous and belongs to a parametric family , where the q-dimensional parameter space is neither known nor specified. We proposed a Khmaladze martingale-transformed type of test (Khmaladze, 1981), adapted to recurrent events. The test statistic combines two likelihood sources of estimation to form a parametric empirical process: (1) a product-limit nonparametric maximum likelihood estimator (NPMLE; Peña et al., 2001a) that is a consistent estimator of F, say, and (2) a point process likelihood estimator (Jacod, 1974/1975). These estimators are combined to construct a Kolmogorov-Smirnov (KS) type of test (Kolmogorov 1933; Smirnov, 1933). Empirical process and martingale weak convergence frameworks are utilized for theoretical derivations and motivational justification of the proposed transformation. A simulation study is conducted for performance assessment, and the test is applied to a problem investigated by Proschan (1963) on air-conditioning failure in a fleet of Boeing 720 jets.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"38 1","pages":"318 - 341"},"PeriodicalIF":0.8,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2019.1648920","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47419143","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}
引用次数: 1
Determination of multiple dependent state repetitive group sampling plan based on the process capability index 基于过程能力指数的多依赖状态重复群抽样方案的确定
IF 0.8 4区 数学
Sequential Analysis-Design Methods and Applications Pub Date : 2019-07-03 DOI: 10.1080/07474946.2019.1648930
S. Balamurali, M. Aslam
{"title":"Determination of multiple dependent state repetitive group sampling plan based on the process capability index","authors":"S. Balamurali, M. Aslam","doi":"10.1080/07474946.2019.1648930","DOIUrl":"https://doi.org/10.1080/07474946.2019.1648930","url":null,"abstract":"Abstract In this article, we propose a sampling plan called a multiple dependent state repetitive group sampling plan for variable inspection based on the process capability index Cpk. The proposed sampling plan is applicable for the inspection of normally distributed quality characteristics when both mean and variance are assumed to be unknown. This new plan under variable inspection will be very useful particularly in compliance testing. Tables are also constructed for the determination of optimal parameters for easy selection and implementation of the plan. The optimal parameters can be determined by using the approach of two points on the operating characteristic curve. Symmetric and asymmetric cases based on the fraction nonconforming by the lower and the upper specification limits are also considered. Advantages of the proposed plan are also discussed. It is also shown that the proposed plan outperforms other existing sampling plans under variable inspection.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"38 1","pages":"385 - 399"},"PeriodicalIF":0.8,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2019.1648930","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49465849","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}
引用次数: 12
Estimation of common change point and isolation of changed panels after sequential detection 序列检测后常见变化点的估计和变化面板的隔离
IF 0.8 4区 数学
Sequential Analysis-Design Methods and Applications Pub Date : 2019-07-03 DOI: 10.1080/07474946.2020.1726685
Yanhong Wu
{"title":"Estimation of common change point and isolation of changed panels after sequential detection","authors":"Yanhong Wu","doi":"10.1080/07474946.2020.1726685","DOIUrl":"https://doi.org/10.1080/07474946.2020.1726685","url":null,"abstract":"Abstract Quick detection of common changes is critical in sequential monitoring of multistream data where a common change is a change that only occurs in a portion of panels. After a common change is detected by using a combined cumulative sum Shiryaev-Roberts (CUSUM-SR) procedure, we first study the joint distribution for values of the CUSUM process and the estimated delay detection time for the unchanged panels. A Benjamini-Hochberg (BH) method using the asymptotic exponential property for the CUSUM process is developed to isolate the changed panels with control on the false discovery rate (FDR). The common change point is then estimated based on the isolated changed panels. Simulation results show that the proposed method can also control the false non-discovery rate (FNR) by properly selecting the FDR.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"39 1","pages":"52 - 64"},"PeriodicalIF":0.8,"publicationDate":"2019-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2020.1726685","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47011227","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}
引用次数: 9
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