Pub Date : 2021-01-14DOI: 10.1080/07474946.2021.1847964
Stephen M. Scariano, Jillian E. Parker
Abstract Statistical evidence is presented to answer the title question using graphical tools from process behavior charting as well as ranking methods based on principal component analysis. These tools provide strong data evidence to answer the question convincingly.
{"title":"Using principal component analysis and process behavior charting to answer “Is Secretariat the fastest U.S. racing thoroughbred to date?”","authors":"Stephen M. Scariano, Jillian E. Parker","doi":"10.1080/07474946.2021.1847964","DOIUrl":"https://doi.org/10.1080/07474946.2021.1847964","url":null,"abstract":"Abstract Statistical evidence is presented to answer the title question using graphical tools from process behavior charting as well as ranking methods based on principal component analysis. These tools provide strong data evidence to answer the question convincingly.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"40 1","pages":"46 - 60"},"PeriodicalIF":0.8,"publicationDate":"2021-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2021.1847964","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45320344","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 : 2021-01-14DOI: 10.1080/07474946.2021.1847960
Murat Sagir, V. Saglam
Abstract We aim to determine the traffic density of the system as a control method in queuing systems and to keep it at the desired level. This article expands the sequential probability ratio test (SPRT) method in the heterogeneous server queuing system, which gives more accurate results in modeling a real-life case. Controlling the traffic density of the heterogeneous server queuing system can be used to determine optimal policies for the system.
{"title":"Testing traffic density of a heterogeneous stochastic queueing system using SPRT","authors":"Murat Sagir, V. Saglam","doi":"10.1080/07474946.2021.1847960","DOIUrl":"https://doi.org/10.1080/07474946.2021.1847960","url":null,"abstract":"Abstract We aim to determine the traffic density of the system as a control method in queuing systems and to keep it at the desired level. This article expands the sequential probability ratio test (SPRT) method in the heterogeneous server queuing system, which gives more accurate results in modeling a real-life case. Controlling the traffic density of the heterogeneous server queuing system can be used to determine optimal policies for the system.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"40 1","pages":"32 - 45"},"PeriodicalIF":0.8,"publicationDate":"2021-01-14","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2021.1847960","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47228528","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 : 2021-01-02DOI: 10.1080/07474946.2021.1847969
D. Politis, V. Vasiliev, S. Vorobeychikov
Abstract The optimal parameter estimation problem is considered. The optimization problem is solved in the general problem statement. A model-free approach is applied and supposes no knowledge of the model that the parameter to be estimated belongs to. Optimality of the considered estimators in the sense of a special type risk function is established. The considered risk function makes it possible to optimize the asymptotic variances of the estimators and is used for sample size estimation. Applications for optimization of the truncated parameter estimators of heavy-tailed indexes of distributions, such as Pareto type, Cauchy, and log-gamma, are presented. A class of these estimators is introduced having guaranteed accuracy based on a sample of fixed size. Simulation results confirm theoretical results.
{"title":"Optimal index estimation of heavy-tailed distributions","authors":"D. Politis, V. Vasiliev, S. Vorobeychikov","doi":"10.1080/07474946.2021.1847969","DOIUrl":"https://doi.org/10.1080/07474946.2021.1847969","url":null,"abstract":"Abstract The optimal parameter estimation problem is considered. The optimization problem is solved in the general problem statement. A model-free approach is applied and supposes no knowledge of the model that the parameter to be estimated belongs to. Optimality of the considered estimators in the sense of a special type risk function is established. The considered risk function makes it possible to optimize the asymptotic variances of the estimators and is used for sample size estimation. Applications for optimization of the truncated parameter estimators of heavy-tailed indexes of distributions, such as Pareto type, Cauchy, and log-gamma, are presented. A class of these estimators is introduced having guaranteed accuracy based on a sample of fixed size. Simulation results confirm theoretical results.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"40 1","pages":"125 - 147"},"PeriodicalIF":0.8,"publicationDate":"2021-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2021.1847969","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42522937","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 : 2020-10-01DOI: 10.1080/07474946.2020.1826786
N. Mukhopadhyay, Zhe Wang
Abstract Purely sequential estimation for unknown mean ( ) in a normal population having an unknown variance ( ) when observations are gathered in groups has been recently discussed in Mukhopadhyay and Wang (2020). In this article, we briefly revisit two fundamental problems on sequential estimation: (i) the fixed-width confidence interval (FWCI) estimation problem and (ii) the minimum risk point estimation (MRPE) problem. However, we substitute the estimators defining the stopping boundaries with newly constructed unbiased and consistent estimators under permutations within each group. These new estimators incorporated in the definition of the stopping boundaries have led to tighter estimation of requisite optimal fixed sample sizes. We have analyzed the first-order and second-order asymptotic properties under appropriate requirements on the pilot size. Large-scale computer simulations and substantial data analysis have validated such first-order and second-order results. The methodologies are illustrated with the help of time series data on offshore wind energy.
{"title":"Purely sequential estimation problems for the mean of a normal population by sampling in groups under permutations within each group and illustrations","authors":"N. Mukhopadhyay, Zhe Wang","doi":"10.1080/07474946.2020.1826786","DOIUrl":"https://doi.org/10.1080/07474946.2020.1826786","url":null,"abstract":"Abstract Purely sequential estimation for unknown mean ( ) in a normal population having an unknown variance ( ) when observations are gathered in groups has been recently discussed in Mukhopadhyay and Wang (2020). In this article, we briefly revisit two fundamental problems on sequential estimation: (i) the fixed-width confidence interval (FWCI) estimation problem and (ii) the minimum risk point estimation (MRPE) problem. However, we substitute the estimators defining the stopping boundaries with newly constructed unbiased and consistent estimators under permutations within each group. These new estimators incorporated in the definition of the stopping boundaries have led to tighter estimation of requisite optimal fixed sample sizes. We have analyzed the first-order and second-order asymptotic properties under appropriate requirements on the pilot size. Large-scale computer simulations and substantial data analysis have validated such first-order and second-order results. The methodologies are illustrated with the help of time series data on offshore wind energy.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"39 1","pages":"484 - 519"},"PeriodicalIF":0.8,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2020.1826786","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44976966","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 : 2020-10-01DOI: 10.1080/07474946.2020.1826785
Leng-Cheng Hwang
Abstract The problem of sequential estimation of the mean with quadratic loss and fixed cost per observation is considered within the Bayesian framework. A robust sequential procedure, not depending on the distributions of outcome variables and the prior, in the Bayes sequential estimation is investigated. In the present article, the second-order approximations to the expected sample size and the Bayes risk of the robust sequential procedure are obtained for the arbitrary distributions of outcome variables and the prior. The second-order efficiency is further discussed in an example.
{"title":"Second-order approximations of a robust sequential procedure in Bayes sequential estimation","authors":"Leng-Cheng Hwang","doi":"10.1080/07474946.2020.1826785","DOIUrl":"https://doi.org/10.1080/07474946.2020.1826785","url":null,"abstract":"Abstract The problem of sequential estimation of the mean with quadratic loss and fixed cost per observation is considered within the Bayesian framework. A robust sequential procedure, not depending on the distributions of outcome variables and the prior, in the Bayes sequential estimation is investigated. In the present article, the second-order approximations to the expected sample size and the Bayes risk of the robust sequential procedure are obtained for the arbitrary distributions of outcome variables and the prior. The second-order efficiency is further discussed in an example.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"39 1","pages":"467 - 483"},"PeriodicalIF":0.8,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2020.1826785","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42556836","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 : 2020-10-01DOI: 10.1080/07474946.2020.1826796
Junzhuo Chen, Seong-Hee Kim, Yao Xie
Abstract We present an efficient score statistic, called the statistic, to detect the emergence of a spatially and temporally correlated signal from either fixed-sample or sequential data. The signal may cause a mean shift and/or a change in the covariance structure. The score statistic can capture both the spatial and temporal structures of the change and hence is particularly powerful in detecting weak signals. The score statistic is computationally efficient and statistically powerful. Our main theoretical contribution is accurate analytical approximations to the false alarm rate of the detection procedures, which can be used to calibrate the threshold analytically. Numerical experiments on simulated and real data, as well as a case study of water quality monitoring using sensor networks, demonstrate the good performance of our procedure.
{"title":": A score statistic for spatiotemporal change point detection","authors":"Junzhuo Chen, Seong-Hee Kim, Yao Xie","doi":"10.1080/07474946.2020.1826796","DOIUrl":"https://doi.org/10.1080/07474946.2020.1826796","url":null,"abstract":"Abstract We present an efficient score statistic, called the statistic, to detect the emergence of a spatially and temporally correlated signal from either fixed-sample or sequential data. The signal may cause a mean shift and/or a change in the covariance structure. The score statistic can capture both the spatial and temporal structures of the change and hence is particularly powerful in detecting weak signals. The score statistic is computationally efficient and statistically powerful. Our main theoretical contribution is accurate analytical approximations to the false alarm rate of the detection procedures, which can be used to calibrate the threshold analytically. Numerical experiments on simulated and real data, as well as a case study of water quality monitoring using sensor networks, demonstrate the good performance of our procedure.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"39 1","pages":"563 - 592"},"PeriodicalIF":0.8,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2020.1826796","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44746910","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 : 2020-10-01DOI: 10.1080/07474946.2020.1826795
Samrat Nath, Jingxian Wu
Abstract We study the sequential quickest change point detection for systems with multiple possible postchange models. A change point is the time instant at which the distribution of a random process changes. In many practical applications, the prechange model can be easily obtained, yet the postchange distribution is unknown due to the unexpected nature of the change. In this article, we consider the case that the postchange model is from a finite set of possible models. The objective is to minimize the average detection delay (ADD), subject to upper bounds on the probability of false alarm (PFA). Two different quickest change detection algorithms are proposed under Bayesian and non-Bayesian settings. Under the Bayesian setting, the prior probabilities of the change point and prior probabilities of possible postchange models are assumed to be known, yet this information is not available under the non-Bayesian setting. Theoretical analysis is performed to quantify the analytical performance of the proposed algorithms in terms of exact or asymptotic bounds on PFA and ADD. It is shown through theoretical analysis that when PFA is small, both algorithms are asymptotically optimal in terms of ADD minimization for a given PFA upper bound. Numerical results demonstrate that the proposed algorithms outperform existing algorithms in the literature.
{"title":"Quickest change point detection with multiple postchange models","authors":"Samrat Nath, Jingxian Wu","doi":"10.1080/07474946.2020.1826795","DOIUrl":"https://doi.org/10.1080/07474946.2020.1826795","url":null,"abstract":"Abstract We study the sequential quickest change point detection for systems with multiple possible postchange models. A change point is the time instant at which the distribution of a random process changes. In many practical applications, the prechange model can be easily obtained, yet the postchange distribution is unknown due to the unexpected nature of the change. In this article, we consider the case that the postchange model is from a finite set of possible models. The objective is to minimize the average detection delay (ADD), subject to upper bounds on the probability of false alarm (PFA). Two different quickest change detection algorithms are proposed under Bayesian and non-Bayesian settings. Under the Bayesian setting, the prior probabilities of the change point and prior probabilities of possible postchange models are assumed to be known, yet this information is not available under the non-Bayesian setting. Theoretical analysis is performed to quantify the analytical performance of the proposed algorithms in terms of exact or asymptotic bounds on PFA and ADD. It is shown through theoretical analysis that when PFA is small, both algorithms are asymptotically optimal in terms of ADD minimization for a given PFA upper bound. Numerical results demonstrate that the proposed algorithms outperform existing algorithms in the literature.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"39 1","pages":"543 - 562"},"PeriodicalIF":0.8,"publicationDate":"2020-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2020.1826795","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"49332164","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 : 2020-09-05DOI: 10.1080/07474946.2020.1826792
B. Levin, C. Leu
Abstract We exhibit some strong positivity properties of a certain function that implies a key inequality that in turn implies the lower bound formula for the probability of correct selection in the Levin-Robbins-Leu family of sequential subset selection procedures for binary outcomes. These properties provide a more direct and comprehensive demonstration of the key inequality than was discussed in Levin and Leu (2013a).
{"title":"Positivity of cumulative sums for multi-index function components explains the lower bound formula in the Levin-Robbins-Leu family of sequential subset selection procedures","authors":"B. Levin, C. Leu","doi":"10.1080/07474946.2020.1826792","DOIUrl":"https://doi.org/10.1080/07474946.2020.1826792","url":null,"abstract":"Abstract We exhibit some strong positivity properties of a certain function that implies a key inequality that in turn implies the lower bound formula for the probability of correct selection in the Levin-Robbins-Leu family of sequential subset selection procedures for binary outcomes. These properties provide a more direct and comprehensive demonstration of the key inequality than was discussed in Levin and Leu (2013a).","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"39 1","pages":"520 - 542"},"PeriodicalIF":0.8,"publicationDate":"2020-09-05","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2020.1826792","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"59425334","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 : 2020-07-02DOI: 10.1080/07474946.2020.1823194
N. Kumar, R. Singh
Abstract Geometric charts have an important role in monitoring fraction nonconforming in high-yield processes where the rate of nonconforming is very low, say, parts per million. Currently, the average number of inspected items (ANI) to give an out-of-control (OOC) signal is preferred to the average run length (ARL) in designing and evaluating geometric charts. The ANI carries more information than the ARL because the former considers the number of inspected units contained in each charting point until a signal occurs. Like ARL, the ANI function possesses bias, which results that the chart requiring more items to be inspected to detect an OOC signal rather than a false alarm. In this article, an ANI-unbiased geometric chart is proposed and its performance is compared with the existing ARL-unbiased chart. The study shows that neither is better than the other for all shifts in the process parameter. The study is also extended to the CCCG chart where a group of samples is inspected instead of individual items.
{"title":"A comparative study of ANI- and ARL-unbiased geometric and CCCG control charts","authors":"N. Kumar, R. Singh","doi":"10.1080/07474946.2020.1823194","DOIUrl":"https://doi.org/10.1080/07474946.2020.1823194","url":null,"abstract":"Abstract Geometric charts have an important role in monitoring fraction nonconforming in high-yield processes where the rate of nonconforming is very low, say, parts per million. Currently, the average number of inspected items (ANI) to give an out-of-control (OOC) signal is preferred to the average run length (ARL) in designing and evaluating geometric charts. The ANI carries more information than the ARL because the former considers the number of inspected units contained in each charting point until a signal occurs. Like ARL, the ANI function possesses bias, which results that the chart requiring more items to be inspected to detect an OOC signal rather than a false alarm. In this article, an ANI-unbiased geometric chart is proposed and its performance is compared with the existing ARL-unbiased chart. The study shows that neither is better than the other for all shifts in the process parameter. The study is also extended to the CCCG chart where a group of samples is inspected instead of individual items.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"39 1","pages":"399 - 416"},"PeriodicalIF":0.8,"publicationDate":"2020-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2020.1823194","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41740689","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 : 2020-07-02DOI: 10.1080/07474946.2020.1823195
A. Walker
Abstract Postmarketing safety surveillance studies address two actionable questions: (1) Is the test product riskier than a standard? (2) Is the risk associated with the test product within some tolerable margin by comparison to the standard? Established techniques, not commonly applied to the setting of such complementary one-sided hypotheses, lead to useful conclusions in practice. For two-group studies, a search over possible one-sided binomial test results yields sample sizes that guarantee that the confidence bounds exclude one or the other of the hypotheses. With continuous monitoring, simple curtailment reduces the sample size. Point and interval estimates follow from the binomial distribution of events at the end of the study or from component negative binomials for crossing a bound of simple curtailment with continuous monitoring and earlier stopping. An asymptotic derivation corresponds to the problem of constructing a confidence interval that is smaller than the distance between the parameter values for tolerable excess and the absence of excess risk. Studies with guaranteed rejection of one of the pair of complementary hypotheses are somewhat larger than corresponding studies of a single hypothesis under usual power requirements, but the increase may be tolerable in return for certainty that there will be an actionable conclusion.
{"title":"Complementary hypotheses in safety surveillance","authors":"A. Walker","doi":"10.1080/07474946.2020.1823195","DOIUrl":"https://doi.org/10.1080/07474946.2020.1823195","url":null,"abstract":"Abstract Postmarketing safety surveillance studies address two actionable questions: (1) Is the test product riskier than a standard? (2) Is the risk associated with the test product within some tolerable margin by comparison to the standard? Established techniques, not commonly applied to the setting of such complementary one-sided hypotheses, lead to useful conclusions in practice. For two-group studies, a search over possible one-sided binomial test results yields sample sizes that guarantee that the confidence bounds exclude one or the other of the hypotheses. With continuous monitoring, simple curtailment reduces the sample size. Point and interval estimates follow from the binomial distribution of events at the end of the study or from component negative binomials for crossing a bound of simple curtailment with continuous monitoring and earlier stopping. An asymptotic derivation corresponds to the problem of constructing a confidence interval that is smaller than the distance between the parameter values for tolerable excess and the absence of excess risk. Studies with guaranteed rejection of one of the pair of complementary hypotheses are somewhat larger than corresponding studies of a single hypothesis under usual power requirements, but the increase may be tolerable in return for certainty that there will be an actionable conclusion.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":"39 1","pages":"417 - 430"},"PeriodicalIF":0.8,"publicationDate":"2020-07-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://sci-hub-pdf.com/10.1080/07474946.2020.1823195","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42325846","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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