Proportions based on the binominal distribution are often compared in clinical tests. Biostatisticians often use the Fisher exact test in order to show the superiority of the binominal proportions of a test drug. Kawasaki and Miyaoka (2012) derived an accurate expression for a new index: θ = P (π1,post > π2,post | X1, X2) within a Bayesian framework. In this paper, we investigate the relationship between θ proposed by Kawasaki and Miyaoka (2012) and the p-value of Fisher’s exact test (Fisher (1934)). We show that these two indicators are equivalent under certain conditions.
基于二项分布的比例在临床试验中经常被比较。生物统计学家经常使用费雪精确检验，以显示试验药物的二项比例的优越性。Kawasaki and Miyaoka(2012)在贝叶斯框架下导出了一个新指标的精确表达式:θ = P (π1,post > π2,post | X1, X2)。本文研究了Kawasaki and Miyaoka(2012)提出的θ与Fisher精确检验(Fisher(1934))的p值之间的关系。我们证明这两个指标在一定条件下是等价的。
{"title":"On the Bayesian Index of Superiority and the p-Value of the Fisher Exact Test for Binomial Proportions","authors":"K. Kawasaki, Asanao Shimokawa, E. Miyaoka","doi":"10.14490/JJSS.44.73","DOIUrl":"https://doi.org/10.14490/JJSS.44.73","url":null,"abstract":"Proportions based on the binominal distribution are often compared in clinical tests. Biostatisticians often use the Fisher exact test in order to show the superiority of the binominal proportions of a test drug. Kawasaki and Miyaoka (2012) derived an accurate expression for a new index: θ = P (π1,post > π2,post | X1, X2) within a Bayesian framework. In this paper, we investigate the relationship between θ proposed by Kawasaki and Miyaoka (2012) and the p-value of Fisher’s exact test (Fisher (1934)). We show that these two indicators are equivalent under certain conditions.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122512847","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"GARCH Models: Structure, Statistical Inference and Financial Applications","authors":"修一 永田","doi":"10.11329/JJSSJ.44.243","DOIUrl":"https://doi.org/10.11329/JJSSJ.44.243","url":null,"abstract":"","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114360041","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
{"title":"Introducing Monte Carlo Methods with R","authors":"研吾 鎌谷","doi":"10.11329/JJSSJ.44.241","DOIUrl":"https://doi.org/10.11329/JJSSJ.44.241","url":null,"abstract":"","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"10 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128302354","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Statistical Foundations of Data ScienceNew Perspectives and Challenges in Econophysics and SociophysicsStatistical Learning with SparsityMathematical Foundations of Infinite-Dimensional Statistical ModelsStatistics and Analysis of ShapesMultivariate StatisticsHigh-Dimensional Covariance EstimationPrinciples and Methods for Data ScienceHigh-Dimensional StatisticsHigh-Dimensional ProbabilityHandbook of Financial Econometrics and StatisticsStatistics for High-Dimensional DataRegularization in High-dimensional StatisticsAnalysis of Multivariate and High-Dimensional DataProbability and ComputingLarge Sample Covariance Matrices and High-Dimensional Data AnalysisHigh-Dimensional Data Analysis in Cancer ResearchHandbook of Big Data AnalyticsIntroduction to Clustering Large and High-Dimensional DataAnalyzing High-Dimensional Gene Expression and DNA Methylation Data with RSufficient Dimension ReductionHandbook of Big DataHandbook of Mixture AnalysisHigh Dimensional Probability VIStatistical Analysis for High-Dimensional DataHigh-Dimensional ProbabilitySpectral Analysis of Large Dimensional Random MatricesBig Data AnalyticsIntroduction to High-Dimensional StatisticsGeometric Structure of High-Dimensional Data and Dimensionality ReductionApplied Biclustering Methods for Big and High-Dimensional Data Using RBig and Complex Data AnalysisHigh-dimensional Data AnalysisFunctional Statistics and Related FieldsHandbook of Data VisualizationNonlinear Dimensionality ReductionModern Statistics for Modern BiologySparse Modeling for Image and Vision ProcessingModeling and Stochastic Learning for Forecasting in High DimensionsContributions to Fault Detection and Diagnosis with High-dimensional Data
{"title":"Statistics for High-Dimensional Data: Methods, Theory and Applications","authors":"秀俊 松井","doi":"10.11329/jjssj.44.247","DOIUrl":"https://doi.org/10.11329/jjssj.44.247","url":null,"abstract":"Statistical Foundations of Data ScienceNew Perspectives and Challenges in Econophysics and SociophysicsStatistical Learning with SparsityMathematical Foundations of Infinite-Dimensional Statistical ModelsStatistics and Analysis of ShapesMultivariate StatisticsHigh-Dimensional Covariance EstimationPrinciples and Methods for Data ScienceHigh-Dimensional StatisticsHigh-Dimensional ProbabilityHandbook of Financial Econometrics and StatisticsStatistics for High-Dimensional DataRegularization in High-dimensional StatisticsAnalysis of Multivariate and High-Dimensional DataProbability and ComputingLarge Sample Covariance Matrices and High-Dimensional Data AnalysisHigh-Dimensional Data Analysis in Cancer ResearchHandbook of Big Data AnalyticsIntroduction to Clustering Large and High-Dimensional DataAnalyzing High-Dimensional Gene Expression and DNA Methylation Data with RSufficient Dimension ReductionHandbook of Big DataHandbook of Mixture AnalysisHigh Dimensional Probability VIStatistical Analysis for High-Dimensional DataHigh-Dimensional ProbabilitySpectral Analysis of Large Dimensional Random MatricesBig Data AnalyticsIntroduction to High-Dimensional StatisticsGeometric Structure of High-Dimensional Data and Dimensionality ReductionApplied Biclustering Methods for Big and High-Dimensional Data Using RBig and Complex Data AnalysisHigh-dimensional Data AnalysisFunctional Statistics and Related FieldsHandbook of Data VisualizationNonlinear Dimensionality ReductionModern Statistics for Modern BiologySparse Modeling for Image and Vision ProcessingModeling and Stochastic Learning for Forecasting in High DimensionsContributions to Fault Detection and Diagnosis with High-dimensional Data","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-09-26","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116638551","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A method of the weighted score or penalized likelihood for estimation of ability reducing the asymptotic mean square error is derived. In this method, associated item parameters are assumed to be given or estimated by using a separate calibration sample with the size of an appropriate order. The method can be seen as an extension of the weighted likelihood method that removes the asymptotic bias of the maximum likelihood estimator. In the proposed method, some bias is retained while variance is reduced by using a multiplicative constant for the weight in the weighted score. A lower bound of the constant minimizing the asymptotic mean square error is found under the logistic model having identical items. The lower bound is numerically also shown to be reasonable in the case of the 3-parameter logistic model, with and without model misspecification.
{"title":"Estimation of Ability with Reduced Asymptotic Mean Square Error in Item Response Theory","authors":"H. Ogasawara","doi":"10.14490/JJSS.43.187","DOIUrl":"https://doi.org/10.14490/JJSS.43.187","url":null,"abstract":"A method of the weighted score or penalized likelihood for estimation of ability reducing the asymptotic mean square error is derived. In this method, associated item parameters are assumed to be given or estimated by using a separate calibration sample with the size of an appropriate order. The method can be seen as an extension of the weighted likelihood method that removes the asymptotic bias of the maximum likelihood estimator. In the proposed method, some bias is retained while variance is reduced by using a multiplicative constant for the weight in the weighted score. A lower bound of the constant minimizing the asymptotic mean square error is found under the logistic model having identical items. The lower bound is numerically also shown to be reasonable in the case of the 3-parameter logistic model, with and without model misspecification.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"9 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"117125166","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper proposes a series of specification tests of the dynamic factor model. The Granger non-causality, linear dependency, and omitted explanatory variables tests are presented. All of the tests can be constructed as a natural byproduct of the routine used to calculate the “smoothed” moments, and they do not require the estimation of additional parameters. The actual size and power of the tests are examined in Monte Carlo experiments. The tests are applied to the term structure model of a yield curve.
{"title":"LIKELIHOOD-BASED SPECIFICATION TESTS FOR DYNAMIC FACTOR MODELS","authors":"M. Chiba","doi":"10.14490/JJSS.43.91","DOIUrl":"https://doi.org/10.14490/JJSS.43.91","url":null,"abstract":"This paper proposes a series of specification tests of the dynamic factor model. The Granger non-causality, linear dependency, and omitted explanatory variables tests are presented. All of the tests can be constructed as a natural byproduct of the routine used to calculate the “smoothed” moments, and they do not require the estimation of additional parameters. The actual size and power of the tests are examined in Monte Carlo experiments. The tests are applied to the term structure model of a yield curve.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"18 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133670931","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
A lot of work has been done in two-phase sampling for estimating the population mean of a study variable while considering the non-response at the second phase, see e.g. Khare and Srivastava (1993, 1995), Tabasum and Khan (2004), Singh and Kumar (2008) and Singh et al. (2010). Most authors have used information of a single auxiliary variable while estimating the mean of the study variable, whereas in a practical situation we may require/have auxiliary information on multiple characters. Khare and Sinha (2009, 2011) have used multi-auxiliary characters to estimate the population mean in the presence of nonresponse in the case of simple random sampling. In two-phase sampling, when auxiliary information is obtained at both phases, the nonresponse may occur at both phases as well. In this paper we have proposed a generalized class of estimators for estimating the population mean of a study variable under a two-phase sampling scheme using multi-auxiliary variable(s) in the presence of nonresponse at both phases. The information on all auxiliary variable(s) is not known for the population. The bias and mean square error have been derived for the suggested class. Special cases of the class have also been identified. An empirical study has been conducted for comparing the efficiency of the proposed estimators with a modified version of existing ones.
{"title":"GENERALIZED CLASS OF MEAN ESTIMATORS FOR TWO PHASE SAMPLING IN THE PRESENCE OF NONRESPONSE","authors":"Zahoor Ahmad, Irsa Zafar, Zakia Bano","doi":"10.14490/JJSS.43.163","DOIUrl":"https://doi.org/10.14490/JJSS.43.163","url":null,"abstract":"A lot of work has been done in two-phase sampling for estimating the population mean of a study variable while considering the non-response at the second phase, see e.g. Khare and Srivastava (1993, 1995), Tabasum and Khan (2004), Singh and Kumar (2008) and Singh et al. (2010). Most authors have used information of a single auxiliary variable while estimating the mean of the study variable, whereas in a practical situation we may require/have auxiliary information on multiple characters. Khare and Sinha (2009, 2011) have used multi-auxiliary characters to estimate the population mean in the presence of nonresponse in the case of simple random sampling. In two-phase sampling, when auxiliary information is obtained at both phases, the nonresponse may occur at both phases as well. In this paper we have proposed a generalized class of estimators for estimating the population mean of a study variable under a two-phase sampling scheme using multi-auxiliary variable(s) in the presence of nonresponse at both phases. The information on all auxiliary variable(s) is not known for the population. The bias and mean square error have been derived for the suggested class. Special cases of the class have also been identified. An empirical study has been conducted for comparing the efficiency of the proposed estimators with a modified version of existing ones.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"107 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126801481","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Sometimes Markov chain Monte Carlo (MCMC) procedures work poorly. The identification of this inefficiency is important, but appropriate theoretical tools have not been investigated adequately. For this purpose, we propose the order of degeneracy, which measures the mixing property of an MCMC procedure. As an application, we consider major three sources of inefficiency, one being the fragility of the identification of parameters. We present a numerical simulation to show the effect of each source of inefficiency.
{"title":"THE ORDER OF DEGENERACY OF MARKOV CHAIN MONTE CARLO METHOD","authors":"K. Kamatani","doi":"10.14490/JJSS.43.203","DOIUrl":"https://doi.org/10.14490/JJSS.43.203","url":null,"abstract":"Sometimes Markov chain Monte Carlo (MCMC) procedures work poorly. The identification of this inefficiency is important, but appropriate theoretical tools have not been investigated adequately. For this purpose, we propose the order of degeneracy, which measures the mixing property of an MCMC procedure. As an application, we consider major three sources of inefficiency, one being the fragility of the identification of parameters. We present a numerical simulation to show the effect of each source of inefficiency.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"16 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115540737","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
This paper studies a prediction problem of factor scores with correlationpreserving linear predictors. We deal with three new risk functions that are obtained by modifying some typical risk functions in the literature, and derive optimal correlation-preserving linear predictors with respect to them. A necessary and sufficient condition for an identical equality among the predictors to hold is also derived.
{"title":"OPTIMAL CORRELATION PRESERVING LINEAR PREDICTORS OF FACTOR SCORES IN FACTOR ANALYSIS","authors":"Kazumasa Mori, H. Kurata","doi":"10.14490/JJSS.43.79","DOIUrl":"https://doi.org/10.14490/JJSS.43.79","url":null,"abstract":"This paper studies a prediction problem of factor scores with correlationpreserving linear predictors. We deal with three new risk functions that are obtained by modifying some typical risk functions in the literature, and derive optimal correlation-preserving linear predictors with respect to them. A necessary and sufficient condition for an identical equality among the predictors to hold is also derived.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127625821","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
The Ewens sampling formula is well-known as a distribution of a random partition of the positive integer n. For the number of distinct components of the Ewens sampling formula, we derive its Edgeworth expansion. It is different from the Edgeworth expansion for the sum of independent and identicallydistributed random variables. It contains the digamma function of the parameter of the Ewens sampling formula. Especially, for the random permutation, the Edgeworth expansion contains Euler’s constant. The Edgeworth expansion is examined numericallyusing its graph.
{"title":"EDGEWORTH EXPANSIONS FOR THE NUMBER OF DISTINCT COMPONENTS ASSOCIATED WITH THE EWENS SAMPLING FORMULA","authors":"Hajime Yamato","doi":"10.14490/JJSS.43.17","DOIUrl":"https://doi.org/10.14490/JJSS.43.17","url":null,"abstract":"The Ewens sampling formula is well-known as a distribution of a random partition of the positive integer n. For the number of distinct components of the Ewens sampling formula, we derive its Edgeworth expansion. It is different from the Edgeworth expansion for the sum of independent and identicallydistributed random variables. It contains the digamma function of the parameter of the Ewens sampling formula. Especially, for the random permutation, the Edgeworth expansion contains Euler’s constant. The Edgeworth expansion is examined numericallyusing its graph.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"76 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2013-08-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127286531","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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