Pub Date : 2022-03-26DOI: 10.1080/07474946.2022.2109673
A. 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 the Kiefer-Weiss problems. For the case of observations following a discrete exponential family, we provide algorithms for optimal design in the modified Kiefer-Weiss problem and obtain formulas for evaluating their performance, calculating operating characteristic function, average sample number, and some related characteristics. These formulas cover, as a particular case, sequential probability ratio tests (SPRTs) and their truncated versions, as well as optimal finite-horizon sequential tests. On the basis of the developed algorithms we propose a method of construction of optimal tests and their performance evaluation for the original Kiefer-Weiss problem. All algorithms are implemented as functions in the R programming language and can be downloaded from https://github.com/tosinabase/Kiefer-Weiss, where the code for the binomial, Poisson, and negative binomial distributions is readily available. Finally, we make numerical comparisons of the Kiefer-Weiss solution with the SPRT and the fixed-sample-size test having the same levels of the error probabilities.
{"title":"Design and performance evaluation in Kiefer-Weiss problems when sampling from discrete exponential families","authors":"A. Novikov, Fahil Farkhshatov","doi":"10.1080/07474946.2022.2109673","DOIUrl":"https://doi.org/10.1080/07474946.2022.2109673","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 the Kiefer-Weiss problems. For the case of observations following a discrete exponential family, we provide algorithms for optimal design in the modified Kiefer-Weiss problem and obtain formulas for evaluating their performance, calculating operating characteristic function, average sample number, and some related characteristics. These formulas cover, as a particular case, sequential probability ratio tests (SPRTs) and their truncated versions, as well as optimal finite-horizon sequential tests. On the basis of the developed algorithms we propose a method of construction of optimal tests and their performance evaluation for the original Kiefer-Weiss problem. All algorithms are implemented as functions in the R programming language and can be downloaded from https://github.com/tosinabase/Kiefer-Weiss, where the code for the binomial, Poisson, and negative binomial distributions is readily available. Finally, we make numerical comparisons of the Kiefer-Weiss solution with the SPRT and the fixed-sample-size test having the same levels of the error probabilities.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-03-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44850892","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 : 2022-01-06DOI: 10.1080/07474946.2021.2010404
Soudabe Sajjadipanah, E. Mahmoudi, Mohammadsadegh Zamani
A two-stage procedure in a first-order autoregressive model ðARð1ÞÞ is considered that investigates the point and the interval estimation of parameters based on the least squares estimator. The two-stage procedure is shown to be as effective as the best fixed-sample-size procedure. In this regard, the significant properties of the procedure, such as asymptotic risk efficiency, asymptotic efficiency, and asymptotic consistency, are established. A Monte Carlo simulation study is conducted to compare the performance of the two-stage procedure and the purely sequential procedure. Finally, real-time series data are considered to illustrate the applicability of the two-stage procedure. ARTICLE HISTORY Received 6 May 2020 Revised 14 June 2021 Accepted 5 September 2021
{"title":"Two-stage procedure in a first-order autoregressive process and comparison with a purely sequential procedure","authors":"Soudabe Sajjadipanah, E. Mahmoudi, Mohammadsadegh Zamani","doi":"10.1080/07474946.2021.2010404","DOIUrl":"https://doi.org/10.1080/07474946.2021.2010404","url":null,"abstract":"A two-stage procedure in a first-order autoregressive model ðARð1ÞÞ is considered that investigates the point and the interval estimation of parameters based on the least squares estimator. The two-stage procedure is shown to be as effective as the best fixed-sample-size procedure. In this regard, the significant properties of the procedure, such as asymptotic risk efficiency, asymptotic efficiency, and asymptotic consistency, are established. A Monte Carlo simulation study is conducted to compare the performance of the two-stage procedure and the purely sequential procedure. Finally, real-time series data are considered to illustrate the applicability of the two-stage procedure. ARTICLE HISTORY Received 6 May 2020 Revised 14 June 2021 Accepted 5 September 2021","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-06","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48141187","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 : 2022-01-02DOI: 10.1080/07474946.2022.2043048
Jun Wu, Pei Li, Jia Zhang, Zehao Chen, J. Bao
Abstract In view of the spectrum scarcity of unmanned aerial vehicles’ (UAVs) communication systems, cooperative spectrum sensing (CSS) is used to identify the available spectrum for cognitive UAV networks (CUAVNs). Due to the flexible locations of flying UAVs, we first design an intraframe cooperation way to replace the traditional interframe cooperation to achieve CSS in this article. Considering certain performance requirements in CUAVNs, we perform an in-depth analysis of the relationship among performance indices of sequential probability ratio test (SPRT)-based CSS and approximate the actual detection performance and the stopping time by ignoring the excess over the boundaries and the random walk. Finally, numerical results corroborate the effectiveness and correctness of our theoretical analysis, and comparison results represent the superiority of our proposal.
{"title":"SPRT-based cooperative spectrum sensing with performance requirements in cognitive unmanned aerial vehicle networks (CUAVNs)","authors":"Jun Wu, Pei Li, Jia Zhang, Zehao Chen, J. Bao","doi":"10.1080/07474946.2022.2043048","DOIUrl":"https://doi.org/10.1080/07474946.2022.2043048","url":null,"abstract":"Abstract In view of the spectrum scarcity of unmanned aerial vehicles’ (UAVs) communication systems, cooperative spectrum sensing (CSS) is used to identify the available spectrum for cognitive UAV networks (CUAVNs). Due to the flexible locations of flying UAVs, we first design an intraframe cooperation way to replace the traditional interframe cooperation to achieve CSS in this article. Considering certain performance requirements in CUAVNs, we perform an in-depth analysis of the relationship among performance indices of sequential probability ratio test (SPRT)-based CSS and approximate the actual detection performance and the stopping time by ignoring the excess over the boundaries and the random walk. Finally, numerical results corroborate the effectiveness and correctness of our theoretical analysis, and comparison results represent the superiority of our proposal.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"48700099","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 : 2022-01-02DOI: 10.1080/07474946.2022.2043047
S. Christensen, Tobias Sohr
Abstract This article treats both discrete time and continuous time stopping problems for general Markov processes on the real line with general linear costs as they naturally arise in many problems in sequential decision making. Using an auxiliary function of maximum representation type, conditions are given to guarantee the optimal stopping time to be of threshold type. The optimal threshold is then characterized as the root of that function. For random walks, our results condense in the fact that all combinations of concave increasing payoff functions and convex cost functions lead to a one-sided solution. For Lévy processes, an explicit way to obtain the auxiliary function and the threshold is given by use of the ladder height processes. Lastly, the connection from discrete and continuous problems and possible approximation of the latter via the former is discussed and the results are applied to sequential tests of power one.
{"title":"General optimal stopping with linear cost","authors":"S. Christensen, Tobias Sohr","doi":"10.1080/07474946.2022.2043047","DOIUrl":"https://doi.org/10.1080/07474946.2022.2043047","url":null,"abstract":"Abstract This article treats both discrete time and continuous time stopping problems for general Markov processes on the real line with general linear costs as they naturally arise in many problems in sequential decision making. Using an auxiliary function of maximum representation type, conditions are given to guarantee the optimal stopping time to be of threshold type. The optimal threshold is then characterized as the root of that function. For random walks, our results condense in the fact that all combinations of concave increasing payoff functions and convex cost functions lead to a one-sided solution. For Lévy processes, an explicit way to obtain the auxiliary function and the threshold is given by use of the ladder height processes. Lastly, the connection from discrete and continuous problems and possible approximation of the latter via the former is discussed and the results are applied to sequential tests of power one.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"42333116","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 : 2022-01-02DOI: 10.1080/07474946.2022.2043046
G. Kannan, P. Jeyadurga, S. Balamurali
Abstract The design of a multiple deferred (dependent) state repetitive group sampling plan for exponentiated half-logistic distributed percentile life assurance under time-truncated life test is considered in this article. In this research, tables are provided to choose the design parameters of the proposed plan determined for different percentile ratios using the method of two points on the operating characteristic curve with known shape parameter values. We describe the sampling procedure of the proposed multiple deferred (dependent) state repetitive group sampling plan with real-time data and discuss the effect of misspecification of the shape parameter on lot acceptance probabilities. Based on an economical design of the proposed plan, an optimal plan is determined that satisfies both producer and consumer risks with minimum cost. In addition, the performance of the proposed plan is analyzed and compared with other existing sampling plans under an exponentiated half-logistic lifetime distribution. Finally, conclusions are provided.
{"title":"Economical design of multiple deferred (dependent) state repetitive group sampling plan based on truncated life test under exponentiated half-logistic distribution","authors":"G. Kannan, P. Jeyadurga, S. Balamurali","doi":"10.1080/07474946.2022.2043046","DOIUrl":"https://doi.org/10.1080/07474946.2022.2043046","url":null,"abstract":"Abstract The design of a multiple deferred (dependent) state repetitive group sampling plan for exponentiated half-logistic distributed percentile life assurance under time-truncated life test is considered in this article. In this research, tables are provided to choose the design parameters of the proposed plan determined for different percentile ratios using the method of two points on the operating characteristic curve with known shape parameter values. We describe the sampling procedure of the proposed multiple deferred (dependent) state repetitive group sampling plan with real-time data and discuss the effect of misspecification of the shape parameter on lot acceptance probabilities. Based on an economical design of the proposed plan, an optimal plan is determined that satisfies both producer and consumer risks with minimum cost. In addition, the performance of the proposed plan is analyzed and compared with other existing sampling plans under an exponentiated half-logistic lifetime distribution. Finally, conclusions are provided.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"44130875","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 : 2022-01-02DOI: 10.1080/07474946.2022.2043050
Shuchen Cao, Ruizhi Zhang, Shaofeng Zou
Abstract The problem of sequential hypothesis testing is studied, where samples are taken sequentially, and the goal is to distinguish between the null hypothesis where the samples are generated according to a distribution p and the alternative hypothesis where the samples are generated according to a distribution q. The defender (decision maker) aims to distinguish the two hypotheses using as few samples as possible subject to false alarm constraints. The problem is studied under the adversarial setting, where the data generating distributions under the two hypotheses are manipulated by an adversary, whose goal is to deteriorate the performance of the defender—for example, increasing the probability of error and expected sample sizes—with minimal cost. Specifically, under the null hypothesis, the adversary picks a distribution with cost and under the alternative hypothesis, the adversary picks a distribution with cost This problem is formulated as a non-zero-sum game between the defender and the adversary. A pair of strategies (the adversary’s strategy and the defender’s strategy) is proposed and proved to be a Nash equilibrium pair for the non-zero-sum game between the adversary and the defender asymptotically. The defender’s strategy is a sequential probability ratio test and thus is computationally efficient for practical implementation.
{"title":"Adversarially robust sequential hypothesis testing","authors":"Shuchen Cao, Ruizhi Zhang, Shaofeng Zou","doi":"10.1080/07474946.2022.2043050","DOIUrl":"https://doi.org/10.1080/07474946.2022.2043050","url":null,"abstract":"Abstract The problem of sequential hypothesis testing is studied, where samples are taken sequentially, and the goal is to distinguish between the null hypothesis where the samples are generated according to a distribution p and the alternative hypothesis where the samples are generated according to a distribution q. The defender (decision maker) aims to distinguish the two hypotheses using as few samples as possible subject to false alarm constraints. The problem is studied under the adversarial setting, where the data generating distributions under the two hypotheses are manipulated by an adversary, whose goal is to deteriorate the performance of the defender—for example, increasing the probability of error and expected sample sizes—with minimal cost. Specifically, under the null hypothesis, the adversary picks a distribution with cost and under the alternative hypothesis, the adversary picks a distribution with cost This problem is formulated as a non-zero-sum game between the defender and the adversary. A pair of strategies (the adversary’s strategy and the defender’s strategy) is proposed and proved to be a Nash equilibrium pair for the non-zero-sum game between the adversary and the defender asymptotically. The defender’s strategy is a sequential probability ratio test and thus is computationally efficient for practical implementation.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"45225532","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 : 2022-01-02DOI: 10.1080/07474946.2022.2043049
Yunning Zhong, Ping Xu, Siming Zhong, Juan Ding
Abstract Group testing (pooling) is a commonly used method while screening for rare diseases, especially for large-scale screening. In recent years there has been growing interest in direct analysis of quantitative measures to take advantage of full information. In this study, we develop a pooling procedure for identification of infected specimens and the measurement is quantitative. Exclusive simulations are conducted to investigate the performance of our procedure, “Qpool,” under a variety of scenarios. We also demonstrate its application in routine monitoring of Listeria monocytogenes.
{"title":"A sequential decoding procedure for pooled quantitative measure","authors":"Yunning Zhong, Ping Xu, Siming Zhong, Juan Ding","doi":"10.1080/07474946.2022.2043049","DOIUrl":"https://doi.org/10.1080/07474946.2022.2043049","url":null,"abstract":"Abstract Group testing (pooling) is a commonly used method while screening for rare diseases, especially for large-scale screening. In recent years there has been growing interest in direct analysis of quantitative measures to take advantage of full information. In this study, we develop a pooling procedure for identification of infected specimens and the measurement is quantitative. Exclusive simulations are conducted to investigate the performance of our procedure, “Qpool,” under a variety of scenarios. We also demonstrate its application in routine monitoring of Listeria monocytogenes.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"41568496","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 : 2022-01-02DOI: 10.1080/07474946.2022.2043051
Jun Hu, Dinh Dong Pham
Abstract In this article, we revisit the classic inference problem of minimum risk point estimation for an unknown normal mean when the variance also remains unknown. We propose an alternative three-stage sampling procedure with termination defined via Gini’s mean difference rather than the traditional sample standard deviation. A number of asymptotic properties are investigated both theoretically and empirically. An extensive set of simulations is conducted to demonstrate the remarkable performance of the new procedure. For practical purposes, we also include illustrations using real data sets on the number of days marigold seeds need to flower.
{"title":"Three-stage minimum risk point estimation with termination defined via Gini’s mean difference","authors":"Jun Hu, Dinh Dong Pham","doi":"10.1080/07474946.2022.2043051","DOIUrl":"https://doi.org/10.1080/07474946.2022.2043051","url":null,"abstract":"Abstract In this article, we revisit the classic inference problem of minimum risk point estimation for an unknown normal mean when the variance also remains unknown. We propose an alternative three-stage sampling procedure with termination defined via Gini’s mean difference rather than the traditional sample standard deviation. A number of asymptotic properties are investigated both theoretically and empirically. An extensive set of simulations is conducted to demonstrate the remarkable performance of the new procedure. For practical purposes, we also include illustrations using real data sets on the number of days marigold seeds need to flower.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47025933","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 : 2022-01-02DOI: 10.1080/07474946.2022.2043052
V. Girardin, V. Konev, S. Pergamenchtchikov
Abstract By making use of Kullback-Leibler information, we develop a new approach for the quickest detection problem for general statistical models with dependent observations and unknown postchange distributions; the postchange distribution depends on either unknown informative parameters or unknown nonparametric infinite-dimensional nuisance functions. For such models, we introduce a robust risk as the supremum of the mean detection delay over the class of postchange distributions. On the basis of the window-limited cumulative sum rules developed by Lai in 1988, we propose new detection procedures, making use of the noise density that minimizes the Kullback-Leibler divergence. Then for the constructed detection procedures, we provide sufficient conditions on the considered statistical models that ensure minimax optimality properties with respect to the robust risk. We apply the developed methods to the quick detection problems for both scalar and multivariate autoregressive processes with unknown postchange parameters and unknown noise distributions.
{"title":"Asymptotically optimal robust information-based quick detection for general stochastic models with nonparametric postchange uncertainty","authors":"V. Girardin, V. Konev, S. Pergamenchtchikov","doi":"10.1080/07474946.2022.2043052","DOIUrl":"https://doi.org/10.1080/07474946.2022.2043052","url":null,"abstract":"Abstract By making use of Kullback-Leibler information, we develop a new approach for the quickest detection problem for general statistical models with dependent observations and unknown postchange distributions; the postchange distribution depends on either unknown informative parameters or unknown nonparametric infinite-dimensional nuisance functions. For such models, we introduce a robust risk as the supremum of the mean detection delay over the class of postchange distributions. On the basis of the window-limited cumulative sum rules developed by Lai in 1988, we propose new detection procedures, making use of the noise density that minimizes the Kullback-Leibler divergence. Then for the constructed detection procedures, we provide sufficient conditions on the considered statistical models that ensure minimax optimality properties with respect to the robust risk. We apply the developed methods to the quick detection problems for both scalar and multivariate autoregressive processes with unknown postchange parameters and unknown noise distributions.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2022-01-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"46827078","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 : 2021-12-31DOI: 10.1080/07474946.2022.2082473
Y. Malinovsky, S. Zacks
Abstract We propose two-stage and sequential procedures to estimate the unknown parameter N of a binomial distribution with unknown parameter p, when we reinforce data with an independent sample of a negative binomial experiment having the same p.
{"title":"Two-stage and sequential unbiased estimation of N in binomial trials, when the probability of success p is unknown","authors":"Y. Malinovsky, S. Zacks","doi":"10.1080/07474946.2022.2082473","DOIUrl":"https://doi.org/10.1080/07474946.2022.2082473","url":null,"abstract":"Abstract We propose two-stage and sequential procedures to estimate the unknown parameter N of a binomial distribution with unknown parameter p, when we reinforce data with an independent sample of a negative binomial experiment having the same p.","PeriodicalId":48879,"journal":{"name":"Sequential Analysis-Design Methods and Applications","volume":null,"pages":null},"PeriodicalIF":0.8,"publicationDate":"2021-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"47323310","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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