Pub Date : 2012-12-20DOI: 10.5183/JJSCS.1112001_198
H. Murakami
In this paper, we focus on the univariate two-sample Baumgartner statistic and propose a modification of the B statistic for the shifted-scale parameter. A nonparametric rank test based on the Baumgartner statistic was used to test location, scale, and location-scale parameters. Critical values of the test statistics were evaluated; limiting distributions were derived under the null hypothesis. We investigated the power of the proposed statistics by simulation studies. The results of our simulations indicated that the B2 statistic was superior to the B1 statistic for the shifted scale parameters when the sample sizes were equal under symmetric distributions. The differences between these two statistics were small when the sample sizes were unequal. The B2 statistic is more efficient than other nonparametric statistics.
{"title":"A MAX-TYPE BAUMGARTNER STATISTIC FOR THE TWO-SAMPLE PROBLEM AND ITS POWER COMPARISON","authors":"H. Murakami","doi":"10.5183/JJSCS.1112001_198","DOIUrl":"https://doi.org/10.5183/JJSCS.1112001_198","url":null,"abstract":"In this paper, we focus on the univariate two-sample Baumgartner statistic and propose a modification of the B statistic for the shifted-scale parameter. A nonparametric rank test based on the Baumgartner statistic was used to test location, scale, and location-scale parameters. Critical values of the test statistics were evaluated; limiting distributions were derived under the null hypothesis. We investigated the power of the proposed statistics by simulation studies. The results of our simulations indicated that the B2 statistic was superior to the B1 statistic for the shifted scale parameters when the sample sizes were equal under symmetric distributions. The differences between these two statistics were small when the sample sizes were unequal. The B2 statistic is more efficient than other nonparametric statistics.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"221 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-12-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116410679","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}
Pub Date : 2012-12-01DOI: 10.5183/JJSCS.1105001_196
T. Imada
When all components of a normal mean vector are simultaneously nonnegative or nonpositive, we consider a multivariate test for checking whether at least one component is nonzero based on the likelihood ratio test. First, we assume that the covariance matrix is known. Next, we assume that it is unknown. In both cases, we consider the determination of the critical value for a specified significance level. Since it is difficult to determine the distributions of the likelihood ratio test statistics, we obtain an approximate critical value using two methods, namely computation using grids and Monte Carlo integration. We give numerical examples regarding critical values intended to compare these methods.
{"title":"DETERMINATION OF CRITICAL VALUE OF MULTIVARIATE NORMAL TEST WITH TWO-SIDED ALTERNATIVE BASED ON LIKELIHOOD RATIO TEST","authors":"T. Imada","doi":"10.5183/JJSCS.1105001_196","DOIUrl":"https://doi.org/10.5183/JJSCS.1105001_196","url":null,"abstract":"When all components of a normal mean vector are simultaneously nonnegative or nonpositive, we consider a multivariate test for checking whether at least one component is nonzero based on the likelihood ratio test. First, we assume that the covariance matrix is known. Next, we assume that it is unknown. In both cases, we consider the determination of the critical value for a specified significance level. Since it is difficult to determine the distributions of the likelihood ratio test statistics, we obtain an approximate critical value using two methods, namely computation using grids and Monte Carlo integration. We give numerical examples regarding critical values intended to compare these methods.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"93 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121942095","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}
Pub Date : 2012-12-01DOI: 10.5183/JJSCS.1106001_197
K. Adachi
A data-fitting factor analysis (FA) procedure was recently presented, which is very different from the prevailing covariance-fitting FA. In the former procedure, common and unique factor scores are modeled as fixed unknown parameters, and an unweighted least squares (ULS) function, which is not scale invariant, is minimized for fitting the model to a data matrix. The main purpose of this paper is to settle four remaining problems with data-fitting FA. First, we present a weighted least squares (WLS) procedure which can be scale invariant, and include the above ULS procedure as a special case according to the choice of weights. Second, we prove that the WLS loss function can be minimized, even if raw data are unknown and only their sample covariance matrix is available, despite being a data-fitting approach. Third, we propose an estimator of factor scores that cannot be uniquely determined. Fourth, we empirically compare this data-fitting FA procedure with covariance-fitting FA with respect to recovery of parameter matrices.
{"title":"SOME CONTRIBUTIONS TO DATA-FITTING FACTOR ANALYSIS WITH EMPIRICAL COMPARISONS TO COVARIANCE-FITTING FACTOR ANALYSIS","authors":"K. Adachi","doi":"10.5183/JJSCS.1106001_197","DOIUrl":"https://doi.org/10.5183/JJSCS.1106001_197","url":null,"abstract":"A data-fitting factor analysis (FA) procedure was recently presented, which is very different from the prevailing covariance-fitting FA. In the former procedure, common and unique factor scores are modeled as fixed unknown parameters, and an unweighted least squares (ULS) function, which is not scale invariant, is minimized for fitting the model to a data matrix. The main purpose of this paper is to settle four remaining problems with data-fitting FA. First, we present a weighted least squares (WLS) procedure which can be scale invariant, and include the above ULS procedure as a special case according to the choice of weights. Second, we prove that the WLS loss function can be minimized, even if raw data are unknown and only their sample covariance matrix is available, despite being a data-fitting approach. Third, we propose an estimator of factor scores that cannot be uniquely determined. Fourth, we empirically compare this data-fitting FA procedure with covariance-fitting FA with respect to recovery of parameter matrices.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"89 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122187267","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}
Pub Date : 2012-12-01DOI: 10.5183/JJSCS.1103001_192
T. Kubota, T. Tarumi
In this paper, we investigated the detection of geometric anisotropy (GA) using four directional variograms that produce four sets of parameters. Four angles and corresponding ranges, which are the parameters of the directional variogram models, were used for (cid:12)tting ellipse parameters to detect GA. The (cid:12)tted ellipse indicates the GA determined by the ratio between the semi-major and the semi-minor axes and the rotated angles of the semi-major axis. Another way of detecting GA is to use the likelihood of the data prediction process (the maximum likelihood method). We performed simulation experiments to compare these two methods for detecting GA in addition to a third method that assumes isotropy. Such simulation experiments generate various kinds of GA to evaluate the validity of the three methods. The results of the simulation study showed that, in the case of a small number of data or strong GA, our method provided good results. In contrast, the other two methods only occasionally produced good results.
{"title":"A SIMULATION STUDY OF GEOMETRIC ANISOTROPY DETECTION METHODS","authors":"T. Kubota, T. Tarumi","doi":"10.5183/JJSCS.1103001_192","DOIUrl":"https://doi.org/10.5183/JJSCS.1103001_192","url":null,"abstract":"In this paper, we investigated the detection of geometric anisotropy (GA) using four directional variograms that produce four sets of parameters. Four angles and corresponding ranges, which are the parameters of the directional variogram models, were used for (cid:12)tting ellipse parameters to detect GA. The (cid:12)tted ellipse indicates the GA determined by the ratio between the semi-major and the semi-minor axes and the rotated angles of the semi-major axis. Another way of detecting GA is to use the likelihood of the data prediction process (the maximum likelihood method). We performed simulation experiments to compare these two methods for detecting GA in addition to a third method that assumes isotropy. Such simulation experiments generate various kinds of GA to evaluate the validity of the three methods. The results of the simulation study showed that, in the case of a small number of data or strong GA, our method provided good results. In contrast, the other two methods only occasionally produced good results.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"69 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132549857","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}
Pub Date : 2012-12-01DOI: 10.5183/JJSCS.1103002_193
Kasumi Daidoji, Manabu Iwasaki
When the research outcome is counts of a rare event, Poisson distribution is a first choice to describe the population distribution under study. However in some applications, the zero count would not be observed at all. In such cases the model to be fitted to the data is a zero-truncated Poisson (ZTP) distribution. This distribution is a special case of the more general zero-modified Poisson (ZMP) distribution family. This article discusses estimation procedures for the Poisson parameter of the ZTP model. In particular, performance of confidence intervals in terms of coverage probability is fully examined by Monte Carlo simulations. It is shown that the score-type interval behaves well but the Wald-type interval gives unsatisfactory results if the Poisson mean is small and/or sample size is not so large. A modification of the Wald-type interval is also given, and its performance is investigated by using simulations. The findings are also applicable to ZMP distributions.
{"title":"ON INTERVAL ESTIMATION OF THE POISSON PARAMETER IN A ZERO-TRUNCATED POISSON DISTRIBUTION","authors":"Kasumi Daidoji, Manabu Iwasaki","doi":"10.5183/JJSCS.1103002_193","DOIUrl":"https://doi.org/10.5183/JJSCS.1103002_193","url":null,"abstract":"When the research outcome is counts of a rare event, Poisson distribution is a first choice to describe the population distribution under study. However in some applications, the zero count would not be observed at all. In such cases the model to be fitted to the data is a zero-truncated Poisson (ZTP) distribution. This distribution is a special case of the more general zero-modified Poisson (ZMP) distribution family. This article discusses estimation procedures for the Poisson parameter of the ZTP model. In particular, performance of confidence intervals in terms of coverage probability is fully examined by Monte Carlo simulations. It is shown that the score-type interval behaves well but the Wald-type interval gives unsatisfactory results if the Poisson mean is small and/or sample size is not so large. A modification of the Wald-type interval is also given, and its performance is investigated by using simulations. The findings are also applicable to ZMP distributions.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"129463647","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}
Pub Date : 2011-12-01DOI: 10.5183/JJSCS.1002001_183
M. Iqbal, A. Nishi, Yasuki Kikuchi, K. Nomakuchi
In this article, we derive the observed information matrices for normal mixture models and normal hidden Markov models. We also describe the parametric bootstrap method for the said models. The matrices and the method mentioned above are used to estimate the variance of the maximum likelihood estimates (MLEs) obtained by the Expectation-Maximization (EM) algorithm. Finally, a numerical example is shown using a data set named faithful" given in the free statistical software R.
{"title":"ESTIMATION OF THE VARIANCE FOR THE MAXIMUM LIKELIHOOD ESTIMATES IN NORMAL MIXTURE MODELS AND NORMAL HIDDEN MARKOV MODELS","authors":"M. Iqbal, A. Nishi, Yasuki Kikuchi, K. Nomakuchi","doi":"10.5183/JJSCS.1002001_183","DOIUrl":"https://doi.org/10.5183/JJSCS.1002001_183","url":null,"abstract":"In this article, we derive the observed information matrices for normal mixture models and normal hidden Markov models. We also describe the parametric bootstrap method for the said models. The matrices and the method mentioned above are used to estimate the variance of the maximum likelihood estimates (MLEs) obtained by the Expectation-Maximization (EM) algorithm. Finally, a numerical example is shown using a data set named faithful\" given in the free statistical software R.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"43 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127431477","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}
Pub Date : 2011-12-01DOI: 10.5183/JJSCS.1007001_189
H. Murakami
On testing hypotheses in two-sample problems, the Lepage-type statistic is often used for testing the location and scale parameters. Various Lepage-type statistics have been proposed and discussed by many authors over the course of many years. One of the most famous and powerful Lepage-type statistics is a combination of the Wilcoxon and Mood statistics, namely T . Deriving the exact critical value of the T statistic is difficult when the sample sizes are increased. In that situation, an approximation to the distribution function of a test statistic is extremely important in statistics. The gamma approximation and the saddlepoint approximations are used to evaluate in upper tail probability for the T statistic under finite sample sizes. The accuracy of various approximations to the exact probability of the T statistic is investigated.
{"title":"Approximations to the distribution of a combination of the Wilcoxon and Mood statistics: A numerical comparison","authors":"H. Murakami","doi":"10.5183/JJSCS.1007001_189","DOIUrl":"https://doi.org/10.5183/JJSCS.1007001_189","url":null,"abstract":"On testing hypotheses in two-sample problems, the Lepage-type statistic is often used for testing the location and scale parameters. Various Lepage-type statistics have been proposed and discussed by many authors over the course of many years. One of the most famous and powerful Lepage-type statistics is a combination of the Wilcoxon and Mood statistics, namely T . Deriving the exact critical value of the T statistic is difficult when the sample sizes are increased. In that situation, an approximation to the distribution function of a test statistic is extremely important in statistics. The gamma approximation and the saddlepoint approximations are used to evaluate in upper tail probability for the T statistic under finite sample sizes. The accuracy of various approximations to the exact probability of the T statistic is investigated.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"125798907","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}
Pub Date : 2011-12-01DOI: 10.5183/JJSCS.1008001_190
K. Yamamoto, S. Ando, S. Tomizawa
For square contingency tables with ordered categories, Agresti (2002) considered the ordinal quasi-symmetry (OQS) model and Iki, Tahata and Tomizawa (2009) considered the ridit score type quasi-symmetry (RQS) model. The present paper proposes measures which represent the degree of departure from each of the OQS and RQS models. The proposed measures are expressed by using the Cressie-Read power-divergence or Patil-Taillie diversity index. These measures would be useful for comparing the degrees of departure from OQS and RQS in several tables. The measures are applied to the data of individual’s education and father’s or mother’s education in Japan.
{"title":"MEASURES OF DEPARTURE FROM ORDINAL QUASI-SYMMETRY MODELS FOR SQUARE CONTINGENCY TABLES","authors":"K. Yamamoto, S. Ando, S. Tomizawa","doi":"10.5183/JJSCS.1008001_190","DOIUrl":"https://doi.org/10.5183/JJSCS.1008001_190","url":null,"abstract":"For square contingency tables with ordered categories, Agresti (2002) considered the ordinal quasi-symmetry (OQS) model and Iki, Tahata and Tomizawa (2009) considered the ridit score type quasi-symmetry (RQS) model. The present paper proposes measures which represent the degree of departure from each of the OQS and RQS models. The proposed measures are expressed by using the Cressie-Read power-divergence or Patil-Taillie diversity index. These measures would be useful for comparing the degrees of departure from OQS and RQS in several tables. The measures are applied to the data of individual’s education and father’s or mother’s education in Japan.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"67 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127254730","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}
Pub Date : 2011-12-01DOI: 10.5183/JJSCS.1008002_191
Ping Jing, Liang Zhang, Yiping Tang, Jinfang Wang
In recent years, attention has been focused on estimating average treatment effects in statistics, economics, epidemiology and so on. For example, effects of job training in economics, or comparing treatment effects in epidemiological studies are frequently studied. There is a lot of literature on estimating the average treatment effect of a binary treatment variable under some assumptions. Some of them use parametric methods, and some use semiparametric methods. This paper firstly describes the role of Rubin’s causal model, reviews various methods for estimating the average treatment effects, then proposes one combined method (subclassification matching method) to estimate the average treatment effect. Extensive simulations are carried to compare all the methods. We find that the proposed mixed methods are better than other methods considered here.
{"title":"SUBCLASSIFICATION MATCHING METHOD FOR AVERAGE TREATMENT EFFECT AND A NUMERICAL COMPARISON OF RELATED METHODS","authors":"Ping Jing, Liang Zhang, Yiping Tang, Jinfang Wang","doi":"10.5183/JJSCS.1008002_191","DOIUrl":"https://doi.org/10.5183/JJSCS.1008002_191","url":null,"abstract":"In recent years, attention has been focused on estimating average treatment effects in statistics, economics, epidemiology and so on. For example, effects of job training in economics, or comparing treatment effects in epidemiological studies are frequently studied. There is a lot of literature on estimating the average treatment effect of a binary treatment variable under some assumptions. Some of them use parametric methods, and some use semiparametric methods. This paper firstly describes the role of Rubin’s causal model, reviews various methods for estimating the average treatment effects, then proposes one combined method (subclassification matching method) to estimate the average treatment effect. Extensive simulations are carried to compare all the methods. We find that the proposed mixed methods are better than other methods considered here.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-12-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126584212","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}
Pub Date : 2011-07-15DOI: 10.5183/JJSCS.1005001_187
T. Hamasaki, Tomoyuki Sugimoto, S. Kim
We consider power-transformations to obtain stability and invariance of measurement scale. The transformation discussed here is the normalized form of the power-transformation originally suggested by Schlesselman (1971). The original suggestion is a simple modification of the Box and Cox transformation to scale invariance for measurement units. In addition to discussion on the scale invariance, we study (i) the behaviors of Jacobian of the transformation and (ii) the effect of the modification on the estimates. Then, we show that the modification of the scale invariance improves the performance of estimates, especially the mean estimate. A simulation study is per-formed to evaluate numerically performances of the modified transformation, compared with the normalized Box and Cox transformation.
{"title":"A SIMPLE MODIFICATION OF THE BOX AND COX TRANSFORMATION TO SCALE STABILITY AND INVARIANCE","authors":"T. Hamasaki, Tomoyuki Sugimoto, S. Kim","doi":"10.5183/JJSCS.1005001_187","DOIUrl":"https://doi.org/10.5183/JJSCS.1005001_187","url":null,"abstract":"We consider power-transformations to obtain stability and invariance of measurement scale. The transformation discussed here is the normalized form of the power-transformation originally suggested by Schlesselman (1971). The original suggestion is a simple modification of the Box and Cox transformation to scale invariance for measurement units. In addition to discussion on the scale invariance, we study (i) the behaviors of Jacobian of the transformation and (ii) the effect of the modification on the estimates. Then, we show that the modification of the scale invariance improves the performance of estimates, especially the mean estimate. A simulation study is per-formed to evaluate numerically performances of the modified transformation, compared with the normalized Box and Cox transformation.","PeriodicalId":338719,"journal":{"name":"Journal of the Japanese Society of Computational Statistics","volume":"4 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-07-15","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115181252","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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