Asmussen and Lehtomaa [Distinguishing log‐concavity from heavy tails. Risks 5(10), 2017] introduced an interesting function g which is able to distinguish between log‐convex and log‐concave tail behaviour of distributions, and proposed a randomized estimator for g. In this paper, we show that g can also be seen as a tool to detect gamma distributions or distributions with gamma tail. We construct a more efficient estimator ĝn based on U‐statistics, propose several estimators of the (asymptotic) variance of ĝn, and study their performance by simulations. Finally, the methods are applied to several data sets of daily precipitation.This article is protected by copyright. All rights reserved.
{"title":"A gamma tail statistic and its asymptotics","authors":"Toshiya Iwashita, B. Klar","doi":"10.1111/stan.12316","DOIUrl":"https://doi.org/10.1111/stan.12316","url":null,"abstract":"Asmussen and Lehtomaa [Distinguishing log‐concavity from heavy tails. Risks 5(10), 2017] introduced an interesting function g which is able to distinguish between log‐convex and log‐concave tail behaviour of distributions, and proposed a randomized estimator for g. In this paper, we show that g can also be seen as a tool to detect gamma distributions or distributions with gamma tail. We construct a more efficient estimator ĝn based on U‐statistics, propose several estimators of the (asymptotic) variance of ĝn, and study their performance by simulations. Finally, the methods are applied to several data sets of daily precipitation.This article is protected by copyright. All rights reserved.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"55 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-06-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74111110","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we derive the copula‐graphic estimator (Zheng and Klein) for marginal survival functions using Archimedean copula models based on competing risks data subject to univariate right censoring and prove its uniform consistency and asymptotic properties. We then propose a novel parameter estimation method based on the semi‐competing risks data using Archimedean copula models. Based on our estimation strategy, we propose a new model selection procedure. We also describe an easy way to accommodate possible covariates in data analysis using our strategies. Simulation studies have shown that our parameter estimate outperforms the estimator proposed by Lakhal, Rivest and Abdous for the Hougaard model and the model selection procedure works quite well. We fit a leukemia dataset using our model and end our paper with some discussion.
{"title":"The analysis of semi‐competing risks data using Archimedean copula models","authors":"Antai Wang, Ziyan Guo, Yilong Zhang, Jihua Wu","doi":"10.1111/stan.12311","DOIUrl":"https://doi.org/10.1111/stan.12311","url":null,"abstract":"In this paper, we derive the copula‐graphic estimator (Zheng and Klein) for marginal survival functions using Archimedean copula models based on competing risks data subject to univariate right censoring and prove its uniform consistency and asymptotic properties. We then propose a novel parameter estimation method based on the semi‐competing risks data using Archimedean copula models. Based on our estimation strategy, we propose a new model selection procedure. We also describe an easy way to accommodate possible covariates in data analysis using our strategies. Simulation studies have shown that our parameter estimate outperforms the estimator proposed by Lakhal, Rivest and Abdous for the Hougaard model and the model selection procedure works quite well. We fit a leukemia dataset using our model and end our paper with some discussion.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"12 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73218378","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Ordinary Least Squares Estimator (OLSE) is widely used to estimate parameters in regression analysis. In practice, the assumptions of regression analysis are often not met. The most common problems that break these assumptions are outliers and multicollinearity problems. As a result of these problems, OLSE loses efficiency. Therefore, alternative estimators to OLSE have been proposed to solve these problems. Robust estimators are often used to solve the outlier problem, and biased estimators are often used to solve the multicollinearity problem. These problems do not always occur individually in the real‐world dataset. Therefore, robust biased estimators are proposed for simultaneous solutions to these problems. The aim of this study is to propose Liu‐type Generalized M Estimator as an alternative to the robust biased estimators available in the literature to obtain more efficient results. This estimator gives effective results in the case of outlier and multicollinearity in both dependent and independent variables. The proposed estimator is theoretically compared with other estimators available in the literature. In addition, Monte Carlo simulation and real dataset example are performed to compare the performance of the estimator with existing estimators.
{"title":"Robust Liu‐type Estimator based on GM estimator","authors":"Melike Işilar, Y. M. Bulut","doi":"10.1111/stan.12310","DOIUrl":"https://doi.org/10.1111/stan.12310","url":null,"abstract":"Ordinary Least Squares Estimator (OLSE) is widely used to estimate parameters in regression analysis. In practice, the assumptions of regression analysis are often not met. The most common problems that break these assumptions are outliers and multicollinearity problems. As a result of these problems, OLSE loses efficiency. Therefore, alternative estimators to OLSE have been proposed to solve these problems. Robust estimators are often used to solve the outlier problem, and biased estimators are often used to solve the multicollinearity problem. These problems do not always occur individually in the real‐world dataset. Therefore, robust biased estimators are proposed for simultaneous solutions to these problems. The aim of this study is to propose Liu‐type Generalized M Estimator as an alternative to the robust biased estimators available in the literature to obtain more efficient results. This estimator gives effective results in the case of outlier and multicollinearity in both dependent and independent variables. The proposed estimator is theoretically compared with other estimators available in the literature. In addition, Monte Carlo simulation and real dataset example are performed to compare the performance of the estimator with existing estimators.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"31 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-05-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73854271","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In this paper, we discuss the inference for the competing risks model when the failure times follow Chen distribution. With assumption of two causes of failures, which are partially observed, are considered as independent. The existence and uniqueness of maximum likelihood estimates for model parameters are obtained under generalized progressive hybrid censoring. Also, we discussed the classical and Bayesian inferences of the model parameters under the assumption of restricted and nonrestricted parameters. Performance of classical point and interval estimators are compared with Bayesian point and interval estimators by conducting extensive simulation study. In addition to that, for illustration purpose, a real life example is discussed. Finally, some concluding remarks, regarding the presented model, are made.
{"title":"On partially observed competing risks model for Chen distribution under generalized progressive hybrid censoring","authors":"Kundan Singh, Amulya Kumar Mahto, Y. Tripathi","doi":"10.1111/stan.12308","DOIUrl":"https://doi.org/10.1111/stan.12308","url":null,"abstract":"In this paper, we discuss the inference for the competing risks model when the failure times follow Chen distribution. With assumption of two causes of failures, which are partially observed, are considered as independent. The existence and uniqueness of maximum likelihood estimates for model parameters are obtained under generalized progressive hybrid censoring. Also, we discussed the classical and Bayesian inferences of the model parameters under the assumption of restricted and nonrestricted parameters. Performance of classical point and interval estimators are compared with Bayesian point and interval estimators by conducting extensive simulation study. In addition to that, for illustration purpose, a real life example is discussed. Finally, some concluding remarks, regarding the presented model, are made.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"240 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-05-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"83140976","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Jumps in the paths of efficient asset prices have important economic implications. Motivated by the issue of testing for jumps based on noisy high‐frequency data, we develop a novel spot volatility estimator, which is obtained by minimizing the sum of some Huber loss functions, and use it as an ingredient for jump detection. This type of estimators is uniformly consistent in estimating the spot volatilities of the efficient price at numerous time points. We further demonstrate the consistency of the proposed jump test based on the property of the novel spot volatility estimator. We show that in finite samples, the proposed volatility estimator and the test perform favorably compared to some competitors through Monte Carlo simulations. We also illustrate our methodology with the stock prices of Apple and Microsoft.
{"title":"Testing for jumps with robust spot volatility estimators","authors":"Yucheng Sun","doi":"10.1111/stan.12306","DOIUrl":"https://doi.org/10.1111/stan.12306","url":null,"abstract":"Jumps in the paths of efficient asset prices have important economic implications. Motivated by the issue of testing for jumps based on noisy high‐frequency data, we develop a novel spot volatility estimator, which is obtained by minimizing the sum of some Huber loss functions, and use it as an ingredient for jump detection. This type of estimators is uniformly consistent in estimating the spot volatilities of the efficient price at numerous time points. We further demonstrate the consistency of the proposed jump test based on the property of the novel spot volatility estimator. We show that in finite samples, the proposed volatility estimator and the test perform favorably compared to some competitors through Monte Carlo simulations. We also illustrate our methodology with the stock prices of Apple and Microsoft.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"47 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-05-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89970698","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
We consider designs with t treatments, the ith level of which has ni observations. Four cases are examined: treatment levels both ordered and not, and the design balanced, with all ni equal, and not. A general construction is given that takes observations, typically treatment sums or treatment rank sums, constructs a simple quadratic form and expresses it as a sum of squares of orthogonal contrasts. For the case of ordered treatment levels, the Kruskal–Wallis, Friedman and Durbin tests are recovered by this construction. A dataset where the design is the supplemented balanced, which is an unbalanced design in our terminology, is analyzed. When treatment levels are not ordered the construction also applies. We then focus on Helmert contrasts.
{"title":"Orthogonal Contrasts for both Balanced and Unbalanced Designs and both Ordered and Unordered Treatments","authors":"J. Rayner, G. Livingston","doi":"10.1111/stan.12305","DOIUrl":"https://doi.org/10.1111/stan.12305","url":null,"abstract":"We consider designs with t treatments, the ith level of which has ni observations. Four cases are examined: treatment levels both ordered and not, and the design balanced, with all ni equal, and not. A general construction is given that takes observations, typically treatment sums or treatment rank sums, constructs a simple quadratic form and expresses it as a sum of squares of orthogonal contrasts. For the case of ordered treatment levels, the Kruskal–Wallis, Friedman and Durbin tests are recovered by this construction. A dataset where the design is the supplemented balanced, which is an unbalanced design in our terminology, is analyzed. When treatment levels are not ordered the construction also applies. We then focus on Helmert contrasts.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"34 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-05-16","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87060789","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper considers linear regression models when neither the response variable nor the covariates can be directly observed, but are measured with multiplicative distortion measurement errors. We propose new identifiability conditions for the distortion functions via the varying coefficient models, then moment‐based estimators of parameters in the model are proposed by using the estimated varying coefficient functions. This method does not require the independence condition between the confounding variables and the unobserved response and variables. We establish the connections among the varying coefficient based estimators, the conditional mean calibration and the conditional absolute mean calibration. We study the asymptotic results of these proposed estimators, and discuss their asymptotic efficiencies. Lastly, we make some comparisons among the proposed estimators through the simulation. These methods are applied to analyze a real dataset for an illustration.
{"title":"Linear Regression Models with Multiplicative Distortions under New Identifiability Conditions","authors":"Jun Zhang, Bingqing Lin, Yan Zhou","doi":"10.1111/stan.12304","DOIUrl":"https://doi.org/10.1111/stan.12304","url":null,"abstract":"This paper considers linear regression models when neither the response variable nor the covariates can be directly observed, but are measured with multiplicative distortion measurement errors. We propose new identifiability conditions for the distortion functions via the varying coefficient models, then moment‐based estimators of parameters in the model are proposed by using the estimated varying coefficient functions. This method does not require the independence condition between the confounding variables and the unobserved response and variables. We establish the connections among the varying coefficient based estimators, the conditional mean calibration and the conditional absolute mean calibration. We study the asymptotic results of these proposed estimators, and discuss their asymptotic efficiencies. Lastly, we make some comparisons among the proposed estimators through the simulation. These methods are applied to analyze a real dataset for an illustration.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"39 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-05-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"75687111","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Joris Pries, Etienne van de Bijl, Jan Klein, Sandjai Bhulai, Rob van der Mei
Before any binary classification model is taken into practice, it is important to validate its performance on a proper test set. Without a frame of reference given by a baseline method, it is impossible to determine if a score is “good” or “bad.” The goal of this paper is to examine all baseline methods that are independent of feature values and determine which model is the “best” and why. By identifying which baseline models are optimal, a crucial selection decision in the evaluation process is simplified. We prove that the recently proposed Dutch Draw baseline is the best input‐independent classifier (independent of feature values) for all order‐invariant measures (independent of sequence order) assuming that the samples are randomly shuffled. This means that the Dutch Draw baseline is the optimal baseline under these intuitive requirements and should therefore be used in practice.
{"title":"The optimal input‐independent baseline for binary classification: The Dutch Draw","authors":"Joris Pries, Etienne van de Bijl, Jan Klein, Sandjai Bhulai, Rob van der Mei","doi":"10.1111/stan.12297","DOIUrl":"https://doi.org/10.1111/stan.12297","url":null,"abstract":"Before any binary classification model is taken into practice, it is important to validate its performance on a proper test set. Without a frame of reference given by a baseline method, it is impossible to determine if a score is “good” or “bad.” The goal of this paper is to examine all baseline methods that are independent of feature values and determine which model is the “best” and why. By identifying which baseline models are optimal, a crucial selection decision in the evaluation process is simplified. We prove that the recently proposed Dutch Draw baseline is the best input‐independent classifier (independent of feature values) for all order‐invariant measures (independent of sequence order) assuming that the samples are randomly shuffled. This means that the Dutch Draw baseline is the optimal baseline under these intuitive requirements and should therefore be used in practice.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"127 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2023-05-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"136012239","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Yu-Hyeong Jang, Jun Zhao, Hyoung-Moon Kim, Kyusang Yu, Sunghoon Kwon, Sunghwan Kim
Maximum likelihood estimation is used widely in classical statistics. However, except in a few cases, it does not have a closed form. Furthermore, it takes time to derive the maximum likelihood estimator (MLE) owing to the use of iterative methods such as Newton–Raphson. Nonetheless, this estimation method has several advantages, chief among them being the invariance property and asymptotic normality. Based on the first approximation to the solution of the likelihood equation, we obtain an estimator that has the same asymptotic behavior as the MLE for multivariate gamma distribution. The newly proposed estimator, denoted as MLECE$$ {mathrm{MLE}}_{mathrm{CE}} $$ , is also in closed form as long as the n$$ sqrt{n} $$ ‐consistent initial estimator is in the closed form. Hence, we develop some closed‐form n$$ sqrt{n} $$ ‐consistent estimators for multivariate gamma distribution to improve the small‐sample property. MLECE$$ {mathrm{MLE}}_{mathrm{CE}} $$ is an alternative to MLE and performs better compared to MLE in terms of computation time, especially for large datasets, and stability. For the bivariate gamma distribution, the MLECE$$ {mathrm{MLE}}_{mathrm{CE}} $$ is over 130 times faster than the MLE, and as the sample size increasing, the MLECE$$ {mathrm{MLE}}_{mathrm{CE}} $$ is over 200 times faster than the MLE. Owing to the instant calculation of the proposed estimator, it can be used in state–space modeling or real‐time processing models.
{"title":"New closed‐form efficient estimator for multivariate gamma distribution","authors":"Yu-Hyeong Jang, Jun Zhao, Hyoung-Moon Kim, Kyusang Yu, Sunghoon Kwon, Sunghwan Kim","doi":"10.1111/stan.12299","DOIUrl":"https://doi.org/10.1111/stan.12299","url":null,"abstract":"Maximum likelihood estimation is used widely in classical statistics. However, except in a few cases, it does not have a closed form. Furthermore, it takes time to derive the maximum likelihood estimator (MLE) owing to the use of iterative methods such as Newton–Raphson. Nonetheless, this estimation method has several advantages, chief among them being the invariance property and asymptotic normality. Based on the first approximation to the solution of the likelihood equation, we obtain an estimator that has the same asymptotic behavior as the MLE for multivariate gamma distribution. The newly proposed estimator, denoted as MLECE$$ {mathrm{MLE}}_{mathrm{CE}} $$ , is also in closed form as long as the n$$ sqrt{n} $$ ‐consistent initial estimator is in the closed form. Hence, we develop some closed‐form n$$ sqrt{n} $$ ‐consistent estimators for multivariate gamma distribution to improve the small‐sample property. MLECE$$ {mathrm{MLE}}_{mathrm{CE}} $$ is an alternative to MLE and performs better compared to MLE in terms of computation time, especially for large datasets, and stability. For the bivariate gamma distribution, the MLECE$$ {mathrm{MLE}}_{mathrm{CE}} $$ is over 130 times faster than the MLE, and as the sample size increasing, the MLECE$$ {mathrm{MLE}}_{mathrm{CE}} $$ is over 200 times faster than the MLE. Owing to the instant calculation of the proposed estimator, it can be used in state–space modeling or real‐time processing models.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"19 1","pages":"555 - 572"},"PeriodicalIF":1.5,"publicationDate":"2023-04-28","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"73572282","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
D. Karlis, Azmi Chutoo, N. Mamode Khan, V. Jowaheer
In spatial count data analysis, modeling with a multilateral lattice structure presents some important challenges. They include both the model construction and the estimation of the model parameters, since the structure accommodates the left, right, top, bottom, and diagonal site effects. Thus, the multilateral spatial process unifies all the popular spatial subclasses that include the unilateral, Rook, Bishop, and Queen models and, hence, makes it suitable for a wide variety of applications. This paper introduces a first‐order multilateral integer‐valued spatial process, based on a binomial thinning mechanism and some innovation term, under both stationary and nonstationary conditions. The estimation of parameters is handled by the conditional maximum likelihood estimation (CML) approach. Simulation experiments are implemented to assess the consistency of the CML estimators in the stationary and nonstationary multilateral spatial model and its subclasses, based on different grid sizes and under both covariate and noncovariate designs. The proposed model, along with its subclasses are applied to real datasets.
{"title":"The Multilateral Spatial Integer‐valued Process of order 1","authors":"D. Karlis, Azmi Chutoo, N. Mamode Khan, V. Jowaheer","doi":"10.1111/stan.12298","DOIUrl":"https://doi.org/10.1111/stan.12298","url":null,"abstract":"In spatial count data analysis, modeling with a multilateral lattice structure presents some important challenges. They include both the model construction and the estimation of the model parameters, since the structure accommodates the left, right, top, bottom, and diagonal site effects. Thus, the multilateral spatial process unifies all the popular spatial subclasses that include the unilateral, Rook, Bishop, and Queen models and, hence, makes it suitable for a wide variety of applications. This paper introduces a first‐order multilateral integer‐valued spatial process, based on a binomial thinning mechanism and some innovation term, under both stationary and nonstationary conditions. The estimation of parameters is handled by the conditional maximum likelihood estimation (CML) approach. Simulation experiments are implemented to assess the consistency of the CML estimators in the stationary and nonstationary multilateral spatial model and its subclasses, based on different grid sizes and under both covariate and noncovariate designs. The proposed model, along with its subclasses are applied to real datasets.","PeriodicalId":51178,"journal":{"name":"Statistica Neerlandica","volume":"07 1","pages":""},"PeriodicalIF":1.5,"publicationDate":"2023-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"85976129","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":3,"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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