Pub Date : 2021-07-03DOI: 10.1080/07474946.2021.1940500
Suthakaran Ratnasingam, Wei Ning
Abstract In this article, we propose a procedure to monitor the structural changes in the penalized regression model for high-dimensional data sequentially. Our approach utilizes a given historical data set to perform both variable selection and estimation simultaneously. The asymptotic properties of the test statistics are established under the null and alternative hypotheses. The finite sample behavior of the monitoring procedure is investigated with simulation studies. The proposed method is applied to a real data set to illustrate the detection procedure.
{"title":"Monitoring sequential structural changes in penalized high-dimensional linear models","authors":"Suthakaran Ratnasingam, Wei Ning","doi":"10.1080/07474946.2021.1940500","DOIUrl":"https://doi.org/10.1080/07474946.2021.1940500","url":null,"abstract":"Abstract In this article, we propose a procedure to monitor the structural changes in the penalized regression model for high-dimensional data sequentially. Our approach utilizes a given historical data set to perform both variable selection and estimation simultaneously. The asymptotic properties of the test statistics are established under the null and alternative hypotheses. The finite sample behavior of the monitoring procedure is investigated with simulation studies. The proposed method is applied to a real data set to illustrate the detection procedure.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"40 1","pages":"381 - 404"},"PeriodicalIF":0.8,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45844882","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 : 2021-07-03DOI: 10.1080/07474946.2021.1940501
S. Knoth
Abstract The average run length (ARL), with its various phenotypes, is the prevailing performance measure for evaluating control charts, or change-point detection schemes. Essentially, the ARL counts the number of observations until the corresponding procedure flags a change. To enable a fair comparison between competing designs, one frequently deploys the steady-state ARL. Differing from the older concept of the zero-state ARL (which assumes that the to-be-detected change occurs immediately at startup or never), the former measure postulates this change’s appearance after reaching some steady state. Considering different notions (primarily conditional and cyclical ones) of the measure, we recapitulate its historical development; provide a critical discussion of its often-careless exploitation, including a few misconceptions; and derive some new mathematical characterizations that permit its easy calculation.
{"title":"Steady-state average run length(s): Methodology, formulas, and numerics","authors":"S. Knoth","doi":"10.1080/07474946.2021.1940501","DOIUrl":"https://doi.org/10.1080/07474946.2021.1940501","url":null,"abstract":"Abstract The average run length (ARL), with its various phenotypes, is the prevailing performance measure for evaluating control charts, or change-point detection schemes. Essentially, the ARL counts the number of observations until the corresponding procedure flags a change. To enable a fair comparison between competing designs, one frequently deploys the steady-state ARL. Differing from the older concept of the zero-state ARL (which assumes that the to-be-detected change occurs immediately at startup or never), the former measure postulates this change’s appearance after reaching some steady state. Considering different notions (primarily conditional and cyclical ones) of the measure, we recapitulate its historical development; provide a critical discussion of its often-careless exploitation, including a few misconceptions; and derive some new mathematical characterizations that permit its easy calculation.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"40 1","pages":"405 - 426"},"PeriodicalIF":0.8,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44651422","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 : 2021-07-03DOI: 10.1080/07474946.2021.1940496
Soumik Banerjee, N. Mukhopadhyay
Abstract We have designed multistage minimum risk point estimation (MRPE) strategies for a function of an unknown mean in a normal population with its variance unknown. These are developed under a weighted power absolute error loss (PAEL) function plus nonlinear cost of sampling by incorporating purely sequential, accelerated sequential, and three-stage estimation methodologies. Crucial asymptotic first-order and asymptotic second-order properties have been proved thoroughly under all three MRPE strategies. Extensive sets of simulations tend to validate nearly all desirable asymptotic properties for small to medium to large optimal fixed sample sizes.
{"title":"Minimum risk point estimation for a function of a normal mean under weighted power absolute error loss plus cost: First-order and second-order asymptotics","authors":"Soumik Banerjee, N. Mukhopadhyay","doi":"10.1080/07474946.2021.1940496","DOIUrl":"https://doi.org/10.1080/07474946.2021.1940496","url":null,"abstract":"Abstract We have designed multistage minimum risk point estimation (MRPE) strategies for a function of an unknown mean in a normal population with its variance unknown. These are developed under a weighted power absolute error loss (PAEL) function plus nonlinear cost of sampling by incorporating purely sequential, accelerated sequential, and three-stage estimation methodologies. Crucial asymptotic first-order and asymptotic second-order properties have been proved thoroughly under all three MRPE strategies. Extensive sets of simulations tend to validate nearly all desirable asymptotic properties for small to medium to large optimal fixed sample sizes.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"40 1","pages":"336 - 369"},"PeriodicalIF":0.8,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46675349","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 : 2021-07-03DOI: 10.1080/07474946.2021.1940499
N. Murugeswari, P. Jeyadurga, S. Balamurali
Abstract Skip-lot sampling plans have the provision of inspecting only a fraction of lots, which reduces time and cost of the inspection. Thus, the skip-lot sampling plan is more cost-effective. The intention of this article is to propose the designing methodology to determine the optimal parameters of skip-lot sampling plan of type 2 with a double sampling plan as a reference plan for resubmitted lots by using two points on the operating characteristic curve. Tables summarize the optimal parameters determined under binomial and Poisson distributions for various combinations of producer quality level and consumer quality level by minimizing the average sample number and subject to satisfying both producer’s risk and consumer’s risk. The execution of the proposed plan is provided with an illustrative example. By comparison, it is proved that the proposed plan is an outstanding plan than the existing skip-lot and conventional sampling plans in terms of probability of acceptance, average sample number, and average total inspection.
{"title":"Optimal design of a skip-lot sampling reinspection plan with a double sampling plan as a reference plan","authors":"N. Murugeswari, P. Jeyadurga, S. Balamurali","doi":"10.1080/07474946.2021.1940499","DOIUrl":"https://doi.org/10.1080/07474946.2021.1940499","url":null,"abstract":"Abstract Skip-lot sampling plans have the provision of inspecting only a fraction of lots, which reduces time and cost of the inspection. Thus, the skip-lot sampling plan is more cost-effective. The intention of this article is to propose the designing methodology to determine the optimal parameters of skip-lot sampling plan of type 2 with a double sampling plan as a reference plan for resubmitted lots by using two points on the operating characteristic curve. Tables summarize the optimal parameters determined under binomial and Poisson distributions for various combinations of producer quality level and consumer quality level by minimizing the average sample number and subject to satisfying both producer’s risk and consumer’s risk. The execution of the proposed plan is provided with an illustrative example. By comparison, it is proved that the proposed plan is an outstanding plan than the existing skip-lot and conventional sampling plans in terms of probability of acceptance, average sample number, and average total inspection.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"40 1","pages":"370 - 380"},"PeriodicalIF":0.8,"publicationDate":"2021-07-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47740115","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 : 2021-06-02DOI: 10.1080/07474946.2021.1912510
Ajit Chaturvedi, Sudeep R. Bapat, Neeraj Joshi
Abstract For the generalized positive exponential family of distributions, the problems of confidence interval estimation, bounded risk point estimation, and minimum risk point estimation of the rth power of unknown parameter θ are handled. Two-stage and purely sequential methodologies are developed for the estimation purpose. Sequential procedures are developed based on the maximum likelihood estimator (MLE) of the parameter. The exact operating characteristics of these procedures are given.
{"title":"Two-stage and sequential procedures for estimation of powers of parameter of a family of distributions","authors":"Ajit Chaturvedi, Sudeep R. Bapat, Neeraj Joshi","doi":"10.1080/07474946.2021.1912510","DOIUrl":"https://doi.org/10.1080/07474946.2021.1912510","url":null,"abstract":"Abstract For the generalized positive exponential family of distributions, the problems of confidence interval estimation, bounded risk point estimation, and minimum risk point estimation of the rth power of unknown parameter θ are handled. Two-stage and purely sequential methodologies are developed for the estimation purpose. Sequential procedures are developed based on the maximum likelihood estimator (MLE) of the parameter. The exact operating characteristics of these procedures are given.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"40 1","pages":"170 - 197"},"PeriodicalIF":0.8,"publicationDate":"2021-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2021.1912510","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49420854","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 : 2021-06-02DOI: 10.1080/07474946.2021.1912515
U. Bandyopadhyay, Suman Sarkar, A. Biswas
Abstract This article deals with fixed-width confidence intervals for the difference between two treatments with ordered categorical data. Related asymptotics are obtained. Procedures are evaluated by simulations, followed by a data illustration.
{"title":"Fixed-width confidence interval for treatment difference in multinomial sampling","authors":"U. Bandyopadhyay, Suman Sarkar, A. Biswas","doi":"10.1080/07474946.2021.1912515","DOIUrl":"https://doi.org/10.1080/07474946.2021.1912515","url":null,"abstract":"Abstract This article deals with fixed-width confidence intervals for the difference between two treatments with ordered categorical data. Related asymptotics are obtained. Procedures are evaluated by simulations, followed by a data illustration.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"40 1","pages":"198 - 208"},"PeriodicalIF":0.8,"publicationDate":"2021-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2021.1912515","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41762635","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 : 2021-06-02DOI: 10.1080/07474946.2021.1912520
H. Ng, Tao Li, Yufei Zeng
Abstract In this article, a class of sequential precedence tests based on ranked set samples (RSS-SPT) with different sequential rank schemes and different α-spending is proposed. The exact null distributions of the proposed RSS-SPT test statistics are derived and the corresponding critical values are tabulated. The performance of the class of RSS-SPT is evaluated in terms of their the power values and their efficiencies by means of the expected stopping location, expected number of failures, and expected total experimental time consumed. The exact power functions and efficiencies of different test procedures under the Lehmann alternative are derived. The performance of RSS-SPT is compared with the nonsequential precedence test based on ranked set samples under the Lehmann alternative based on exact calculation and under the location-shift alternative using Monte Carlo simulations. Conclusions and recommendations are provided based on the numerical results.
{"title":"Sequential procedures for two-sample problem based on early failures from ranked set samples","authors":"H. Ng, Tao Li, Yufei Zeng","doi":"10.1080/07474946.2021.1912520","DOIUrl":"https://doi.org/10.1080/07474946.2021.1912520","url":null,"abstract":"Abstract In this article, a class of sequential precedence tests based on ranked set samples (RSS-SPT) with different sequential rank schemes and different α-spending is proposed. The exact null distributions of the proposed RSS-SPT test statistics are derived and the corresponding critical values are tabulated. The performance of the class of RSS-SPT is evaluated in terms of their the power values and their efficiencies by means of the expected stopping location, expected number of failures, and expected total experimental time consumed. The exact power functions and efficiencies of different test procedures under the Lehmann alternative are derived. The performance of RSS-SPT is compared with the nonsequential precedence test based on ranked set samples under the Lehmann alternative based on exact calculation and under the location-shift alternative using Monte Carlo simulations. Conclusions and recommendations are provided based on the numerical results.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"40 1","pages":"209 - 242"},"PeriodicalIF":0.8,"publicationDate":"2021-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2021.1912520","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42753082","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 : 2021-06-02DOI: 10.1080/07474946.2021.1912503
K. Zamba, P. Tsiamyrtzis
Abstract This article develops a detection framework using Bayesian philosophy by adaptation of Shiryaev's and Roberts' methodology. We propose two unifying versions directly applicable in industrial process control and easily extendable to public health infectious disease surveillance via some data detrending and/or demodulation. The root idea uses the sum of likelihood ratios upon which an optimal stopping criterion is based. It sets a prior on the epoch of a change, allows the flexibility to elicit a prior distribution on other process parameters, and attempts to minimize an expected loss function. A sensitivity analysis is conducted for validation and performance assessment and analytical formulas are derived. The methods are successfully applied to the European Union Centre for Disease Control (ECDC) open-source global COVID-19 incidence data. We further lay out scenarios where interest may switch to the detection of separate outbreaks with similar syndromes during an already evolving epidemic. We view our approach as a toolkit with a potential to augment early reports to sentinels in syndromic surveillance and in biosurveillance.
{"title":"Sequential detection framework for real-time biosurveillance based on Shiryaev-Roberts procedure with illustrations using COVID-19 incidence data","authors":"K. Zamba, P. Tsiamyrtzis","doi":"10.1080/07474946.2021.1912503","DOIUrl":"https://doi.org/10.1080/07474946.2021.1912503","url":null,"abstract":"Abstract This article develops a detection framework using Bayesian philosophy by adaptation of Shiryaev's and Roberts' methodology. We propose two unifying versions directly applicable in industrial process control and easily extendable to public health infectious disease surveillance via some data detrending and/or demodulation. The root idea uses the sum of likelihood ratios upon which an optimal stopping criterion is based. It sets a prior on the epoch of a change, allows the flexibility to elicit a prior distribution on other process parameters, and attempts to minimize an expected loss function. A sensitivity analysis is conducted for validation and performance assessment and analytical formulas are derived. The methods are successfully applied to the European Union Centre for Disease Control (ECDC) open-source global COVID-19 incidence data. We further lay out scenarios where interest may switch to the detection of separate outbreaks with similar syndromes during an already evolving epidemic. We view our approach as a toolkit with a potential to augment early reports to sentinels in syndromic surveillance and in biosurveillance.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"40 1","pages":"149 - 169"},"PeriodicalIF":0.8,"publicationDate":"2021-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2021.1912503","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42264005","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 : 2021-06-02DOI: 10.1080/07474946.2021.1912522
Y. Zhuang, D. Bhattacharjee
Abstract In this article, we address the problem of minimum risk point estimation for the size of a closed population using the weighted squared error loss function with a penalty of cost for each observation under the well-known mark–recapture strategy. In order to achieve minimum risk, a crucial point is to determine the number of items to obtain in the recapture phase. We first develop a purely sequential sampling scheme that will require much less sampling operations without losing accuracy of the estimation. Then, we develop a novel practical accelerated sequential method that will further accelerate the whole recapture process when sampling can be easily done in batches. The stopping rules of both purely sequential and accelerated sequential sampling schemes possess desirable asymptotic properties. All theoretical findings are double validated by extensive data analyses.
{"title":"Minimum risk point estimation of the size of a finite population under mark–recapture strategy","authors":"Y. Zhuang, D. Bhattacharjee","doi":"10.1080/07474946.2021.1912522","DOIUrl":"https://doi.org/10.1080/07474946.2021.1912522","url":null,"abstract":"Abstract In this article, we address the problem of minimum risk point estimation for the size of a closed population using the weighted squared error loss function with a penalty of cost for each observation under the well-known mark–recapture strategy. In order to achieve minimum risk, a crucial point is to determine the number of items to obtain in the recapture phase. We first develop a purely sequential sampling scheme that will require much less sampling operations without losing accuracy of the estimation. Then, we develop a novel practical accelerated sequential method that will further accelerate the whole recapture process when sampling can be easily done in batches. The stopping rules of both purely sequential and accelerated sequential sampling schemes possess desirable asymptotic properties. All theoretical findings are double validated by extensive data analyses.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"40 1","pages":"243 - 258"},"PeriodicalIF":0.8,"publicationDate":"2021-06-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2021.1912522","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44346334","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 : 2021-01-15DOI: 10.1080/07474946.2021.1847940
Nooshin Hakamipour
Abstract In accelerated life testing, the products are tested under high stress conditions and the results are used to draw inferences about the product lifetime under the normal stress condition using a regression model. In this article, optimal k-level constant-stress and step-stress accelerated life tests are compared to the Rayleigh failure data under progressive Type I censoring. The objective is to quantify the advantage of using step-stress testing relative to constant-stress testing. Due to constrained resources in practice, stress durations must be determined carefully at the design stage to run an accelerated life test efficiently. The stress durations directly affect the experimental cost and the estimate precision of the parameters of interest. This article investigates the optimal stress durations based on several (T/C/D/P/R) optimality criteria under the constraint that the total experimental cost does not exceed a prespecified budget. In addition, these criteria are compared together. Under the budget constraint, these two stress loading schemes are compared. Based on the numerical results, the cost constraint reduces cost and time of the test. It is found that the T-optimal design has the lowest cost and time for the unconstrained testing in both stress loading. Finally, a real data set is analyzed for illustrative purposes.
{"title":"Comparison between constant-stress and step-stress accelerated life tests under a cost constraint for progressive type I censoring","authors":"Nooshin Hakamipour","doi":"10.1080/07474946.2021.1847940","DOIUrl":"https://doi.org/10.1080/07474946.2021.1847940","url":null,"abstract":"Abstract In accelerated life testing, the products are tested under high stress conditions and the results are used to draw inferences about the product lifetime under the normal stress condition using a regression model. In this article, optimal k-level constant-stress and step-stress accelerated life tests are compared to the Rayleigh failure data under progressive Type I censoring. The objective is to quantify the advantage of using step-stress testing relative to constant-stress testing. Due to constrained resources in practice, stress durations must be determined carefully at the design stage to run an accelerated life test efficiently. The stress durations directly affect the experimental cost and the estimate precision of the parameters of interest. This article investigates the optimal stress durations based on several (T/C/D/P/R) optimality criteria under the constraint that the total experimental cost does not exceed a prespecified budget. In addition, these criteria are compared together. Under the budget constraint, these two stress loading schemes are compared. Based on the numerical results, the cost constraint reduces cost and time of the test. It is found that the T-optimal design has the lowest cost and time for the unconstrained testing in both stress loading. Finally, a real data set is analyzed for illustrative purposes.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"40 1","pages":"17 - 31"},"PeriodicalIF":0.8,"publicationDate":"2021-01-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2021.1847940","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48723539","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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