Birnbaum-Saunders distribution has received some attention in the statistical literature since its inception. Univariate Birnbaum-Saunders distribution has been used quite effectively in analyzing positively skewed data. Recently, bivariate and multivariate Birnbaum-Saunders distributions have been introduced in the literature. In this paper we propose a new generalization of the multivariate (p-variate) Birnbaum-Saunders distribution based on the multivariate skew normal distribution. It is observed that the proposed distribution is more flexible than the multivariate Birnbaum-Saunders distribution, and the multivariate Birnbaum-Saunders distribution can be obtained as a special case of the proposed model. We obtain the marginal, reciprocal and conditional distributions, and also discuss some other properties. The proposed p-variate distribution has total 3p+ ( p 2 ) parameters. We use the EM algorithm to compute the maximum likelihood estimators of the unknown parameters. One data analysis has been performed for illustrative purposes.
{"title":"A Multivariate Birnbaum-Saunders Distribution Based on the Multivariate Skew Normal Distribution","authors":"A. Jamalizadeh, D. Kundu","doi":"10.14490/JJSS.45.1","DOIUrl":"https://doi.org/10.14490/JJSS.45.1","url":null,"abstract":"Birnbaum-Saunders distribution has received some attention in the statistical literature since its inception. Univariate Birnbaum-Saunders distribution has been used quite effectively in analyzing positively skewed data. Recently, bivariate and multivariate Birnbaum-Saunders distributions have been introduced in the literature. In this paper we propose a new generalization of the multivariate (p-variate) Birnbaum-Saunders distribution based on the multivariate skew normal distribution. It is observed that the proposed distribution is more flexible than the multivariate Birnbaum-Saunders distribution, and the multivariate Birnbaum-Saunders distribution can be obtained as a special case of the proposed model. We obtain the marginal, reciprocal and conditional distributions, and also discuss some other properties. The proposed p-variate distribution has total 3p+ ( p 2 ) parameters. We use the EM algorithm to compute the maximum likelihood estimators of the unknown parameters. One data analysis has been performed for illustrative purposes.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"111 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"132075592","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}
We consider φ -divergence statistics C φ for the test of one factor independence from the other two in an r × s × t contingency table. Statistics C φ include the statistics R a based on the power divergence as a special case. Statistic R 0 is the log likelihood ratio statistic and R 1 is Pearson’s X 2 statistic. Statistic R 2 / 3 corresponds to the statistic for the goodness-of-fit test recommended by Cressie and Read (1984). Statistics C φ have the same chi-square limiting distribution under the hypothesis that one factor and the other two are independent. In this paper, when we assume that the distribution of C φ is continuous, we show the derivation of an expression of approximation based on a multivariate Edgeworth expansion for the distribution of C φ under the hypothesis that one factor and the other two are independent. Using the expression, we propose a new approximation of the distribution of C φ . In addition, on the basis of the approximation, we obtain transformed statistics that improve the speed of convergence to a chi-square limiting distribution of C φ . By numerical comparison in the case of R a , we show that the transformed statistics perform well for a small sample.
{"title":"Improved Transformed Statistics for the Test of One Factor Independence from the Other Two in an r × s × t Contingency Table","authors":"T. Kobe, N. Taneichi, Y. Sekiya","doi":"10.14490/JJSS.45.77","DOIUrl":"https://doi.org/10.14490/JJSS.45.77","url":null,"abstract":"We consider φ -divergence statistics C φ for the test of one factor independence from the other two in an r × s × t contingency table. Statistics C φ include the statistics R a based on the power divergence as a special case. Statistic R 0 is the log likelihood ratio statistic and R 1 is Pearson’s X 2 statistic. Statistic R 2 / 3 corresponds to the statistic for the goodness-of-fit test recommended by Cressie and Read (1984). Statistics C φ have the same chi-square limiting distribution under the hypothesis that one factor and the other two are independent. In this paper, when we assume that the distribution of C φ is continuous, we show the derivation of an expression of approximation based on a multivariate Edgeworth expansion for the distribution of C φ under the hypothesis that one factor and the other two are independent. Using the expression, we propose a new approximation of the distribution of C φ . In addition, on the basis of the approximation, we obtain transformed statistics that improve the speed of convergence to a chi-square limiting distribution of C φ . By numerical comparison in the case of R a , we show that the transformed statistics perform well for a small sample.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2015-09-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127364238","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 new class of generalized two-piece skew normal distribution is introduced here as a two-piece version of the generalized skew normal distribution of Kumar and Anusree (2011). It is shown that the proposed class of distribution will be more suitable for modelling skewed, multimodal data sets. Several properties of the model are studied and the maximum likelihood estimation of the parameters of the distribution is discussed. Further, the practical usefulness of the model is illustrated with the help of certain real life data sets.
{"title":"On Some Properties of a General Class of Two-Piece Skew Normal Distribution","authors":"C. Kumar, M. Anusree","doi":"10.14490/JJSS.44.179","DOIUrl":"https://doi.org/10.14490/JJSS.44.179","url":null,"abstract":"A new class of generalized two-piece skew normal distribution is introduced here as a two-piece version of the generalized skew normal distribution of Kumar and Anusree (2011). It is shown that the proposed class of distribution will be more suitable for modelling skewed, multimodal data sets. Several properties of the model are studied and the maximum likelihood estimation of the parameters of the distribution is discussed. Further, the practical usefulness of the model is illustrated with the help of certain real life data sets.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"24 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114180232","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}
In this paper we study the generalized lower(k)record values arising from the Fréchet distribution. Expressions for the moments and product moments of those generalized lower(k)record values are derived. Some properties of generalized lower(k) record values which characterize the Fréchet distribution have been established. Also some distributional properties of generalized lower(k)record values arising from the Fréchet distribution are considered and used for suggesting an estimator for the shape parameter of the Fréchet distribution. The location and scale parameters are estimated using the Best Linear Unbiased Estimation procedure. Prediction of a future record using the Best Linear Unbiased Predictor has been studied. A real life data set is used to illustrate the results generated in this work.
{"title":"On Generalized Lower(k)record Values from the Fréchet Distribution","authors":"P. Y. Thomas, Jerin Paul","doi":"10.14490/JJSS.44.157","DOIUrl":"https://doi.org/10.14490/JJSS.44.157","url":null,"abstract":"In this paper we study the generalized lower(k)record values arising from the Fréchet distribution. Expressions for the moments and product moments of those generalized lower(k)record values are derived. Some properties of generalized lower(k) record values which characterize the Fréchet distribution have been established. Also some distributional properties of generalized lower(k)record values arising from the Fréchet distribution are considered and used for suggesting an estimator for the shape parameter of the Fréchet distribution. The location and scale parameters are estimated using the Best Linear Unbiased Estimation procedure. Prediction of a future record using the Best Linear Unbiased Predictor has been studied. A real life data set is used to illustrate the results generated in this work.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"59 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"127672618","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}
We consider a complete hierarchical multinomial probit (HMNP) model in which both the regression-coefficient vector and the covariance matrix are assumed to have hierarchical structure and propose an MCMC algorithm for numerically computing the Bayes estimates of the parameters. We show by simulation studies that the covariance matrix is estimated with higher accuracy using the method proposed in this paper than that using an HMNP model in which the covariance matrix is not assumed to have hierarchical structure.
{"title":"Bayes Estimation in the Hierarchical Multinomial Probit Model","authors":"Harunori Mori","doi":"10.14490/JJSS.44.135","DOIUrl":"https://doi.org/10.14490/JJSS.44.135","url":null,"abstract":"We consider a complete hierarchical multinomial probit (HMNP) model in which both the regression-coefficient vector and the covariance matrix are assumed to have hierarchical structure and propose an MCMC algorithm for numerically computing the Bayes estimates of the parameters. We show by simulation studies that the covariance matrix is estimated with higher accuracy using the method proposed in this paper than that using an HMNP model in which the covariance matrix is not assumed to have hierarchical structure.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114921736","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}
In a generalized linear model with binary response, the role of a link function is important to find a model that fits data well. Aranda-Ordaz (1981) proposed a family of link functions that includes a logistic link function and a complementary log-log function. In this paper, we propose a new family of models on the basis of a family of link functions by extending the family proposed by Aranda-Ordaz (1981). We also consider tests to determine whether the new model fits data well. Examples of artificial and real data showing that our new model is more appropriate than the Aranda-Ordaz model are presented.
{"title":"A New Family of Parametric Links for Binomial Generalized Linear Models","authors":"N. Taneichi, Y. Sekiya, Junichiro Toyama","doi":"10.14490/JJSS.44.119","DOIUrl":"https://doi.org/10.14490/JJSS.44.119","url":null,"abstract":"In a generalized linear model with binary response, the role of a link function is important to find a model that fits data well. Aranda-Ordaz (1981) proposed a family of link functions that includes a logistic link function and a complementary log-log function. In this paper, we propose a new family of models on the basis of a family of link functions by extending the family proposed by Aranda-Ordaz (1981). We also consider tests to determine whether the new model fits data well. Examples of artificial and real data showing that our new model is more appropriate than the Aranda-Ordaz model are presented.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"14 2","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121008459","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 addresses the problems of estimating the normal covariance and precision matrices. A commutator subgroup of lower triangular matrices is considered for deriving a class of invariant estimators. The class shows inadmissibility of the best invariant and minimax estimator of the covariance matrix relative to quadratic loss. Also, in estimation of the precision matrix, a dominance result is given for improvement on a minimax estimator relative to the Stein loss.
{"title":"Improvement on the Best Invariant Estimators of the Normal Covariance and Precision Matrices via a Lower Triangular Subgroup","authors":"Hisayuki Tsukuma","doi":"10.14490/JJSS.44.195","DOIUrl":"https://doi.org/10.14490/JJSS.44.195","url":null,"abstract":"This paper addresses the problems of estimating the normal covariance and precision matrices. A commutator subgroup of lower triangular matrices is considered for deriving a class of invariant estimators. The class shows inadmissibility of the best invariant and minimax estimator of the covariance matrix relative to quadratic loss. Also, in estimation of the precision matrix, a dominance result is given for improvement on a minimax estimator relative to the Stein loss.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"28 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2014-12-31","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131555503","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 study proposes a class of realized non-linear stochastic volatility models with asymmetric effects and generalized Student’s t-error distributions by applying three families of power transformation—exponential, modulus, and Yeo-Johnson—to lagged log volatility. The proposed class encompasses a raw version of the realized stochastic volatility model. In the Markov chain Monte Carlo algorithm, an efficient Hamiltonian Monte Carlo (HMC) method is developed to update the latent log volatility and transformation parameter, whereas the other parameters that could not be sampled directly are updated by an efficient Riemann manifold HMC method. Empirical studies on daily returns and four realized volatility estimators of the Tokyo Stock Price Index (TOPIX) over 4-year and 8-year periods demonstrate statistical evidence supporting the incorporation of skew distribution into the error density in the returns and the use of power transformations of lagged log volatility.
本文提出了一类具有非对称效应和广义Student 's t误差分布的非线性随机波动模型，该模型采用三种功率变换族——指数、模数和yeo - johnson -滞后对数波动。所建议的类包含已实现的随机波动模型的原始版本。在马尔可夫链蒙特卡罗算法中，提出了一种有效的哈密顿蒙特卡罗(HMC)方法来更新潜对数波动率和变换参数，而其他不能直接采样的参数则采用有效的Riemann流形HMC方法进行更新。对东京股票价格指数(TOPIX) 4年和8年期间的日收益和四个已实现波动率估计量的实证研究表明，统计证据支持将偏态分布纳入收益的误差密度，并使用滞后对数波动率的幂变换。
{"title":"REALIZED NON-LINEAR STOCHASTIC VOLATILITY MODELS WITH ASYMMETRIC EFFECTS AND GENERALIZED STUDENT'S T -DISTRIBUTIONS","authors":"D. Nugroho, Takayuki Morimoto","doi":"10.14490/JJSS.44.83","DOIUrl":"https://doi.org/10.14490/JJSS.44.83","url":null,"abstract":"This study proposes a class of realized non-linear stochastic volatility models with asymmetric effects and generalized Student’s t-error distributions by applying three families of power transformation—exponential, modulus, and Yeo-Johnson—to lagged log volatility. The proposed class encompasses a raw version of the realized stochastic volatility model. In the Markov chain Monte Carlo algorithm, an efficient Hamiltonian Monte Carlo (HMC) method is developed to update the latent log volatility and transformation parameter, whereas the other parameters that could not be sampled directly are updated by an efficient Riemann manifold HMC method. Empirical studies on daily returns and four realized volatility estimators of the Tokyo Stock Price Index (TOPIX) over 4-year and 8-year periods demonstrate statistical evidence supporting the incorporation of skew distribution into the error density in the returns and the use of power transformations of lagged log volatility.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"49 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":"121646305","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}
For a cumulative link model in the Bayesian context, the posterior distribution cannot be obtained in closed form, and we have to resort to an approximation method. A simple data-augmentation strategy is widely used for that purpose but is known to work poorly. The marginal augmentation procedure and the parameter-expanded data-augmentation procedure are considered to be remedies, but such strategies are still not free from poor convergence. In this paper, we propose a kind of the hybrid Markov chain Monte Carlo strategy. To evaluate the efficiency, a local non-degeneracy is introduced, and we also provide a numerical simulation to show the effect.
{"title":"ASYMPTOTIC PROPERTIES OF MONTE CARLO STRATEGIES FOR A CUMULATIVE LINK MODEL","authors":"K. Kamatani","doi":"10.14490/JJSS.44.1","DOIUrl":"https://doi.org/10.14490/JJSS.44.1","url":null,"abstract":"For a cumulative link model in the Bayesian context, the posterior distribution cannot be obtained in closed form, and we have to resort to an approximation method. A simple data-augmentation strategy is widely used for that purpose but is known to work poorly. The marginal augmentation procedure and the parameter-expanded data-augmentation procedure are considered to be remedies, but such strategies are still not free from poor convergence. In this paper, we propose a kind of the hybrid Markov chain Monte Carlo strategy. To evaluate the efficiency, a local non-degeneracy is introduced, and we also provide a numerical simulation to show the effect.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"66 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":"114572878","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 geographical weighted regression model can be used for visualizing or interpreting the covariate effects that vary with location. This model is usually estimated by a locally weighted regression or a kernel smoothing method, but we can regard the regression coefficients as varying linear coefficients that can be obtained from a global linear regression. There are two types of design vectors, one of which expresses linearity and the other is prepared for nonlinearity, i.e., it assumes a semiparametric surface with varying coefficients. Ridge estimators can then be used to suppress overfitting of the nonlinear part. With a mixed effects model, optimization of the ridge parameters and estimation of the regression parameters can be simultaneously executed. The linear structure of the varying coefficients then provides an asymptotic confidence interval as a function of location, but it is wider than a common pointwise confidence interval. We derive some tests for the varying coefficients and offer two examples using real data to illustrate our methodology. The results of the applied tests are summarized as the uniformity and the linearity of the varying coefficients.
{"title":"ESTIMATING SEMIPARAMETRIC VARYING COEFFICIENTS FOR GEOGRAPHICAL DATA IN A MIXED EFFECTS MODEL","authors":"K. Satoh, T. Tonda","doi":"10.14490/JJSS.44.25","DOIUrl":"https://doi.org/10.14490/JJSS.44.25","url":null,"abstract":"A geographical weighted regression model can be used for visualizing or interpreting the covariate effects that vary with location. This model is usually estimated by a locally weighted regression or a kernel smoothing method, but we can regard the regression coefficients as varying linear coefficients that can be obtained from a global linear regression. There are two types of design vectors, one of which expresses linearity and the other is prepared for nonlinearity, i.e., it assumes a semiparametric surface with varying coefficients. Ridge estimators can then be used to suppress overfitting of the nonlinear part. With a mixed effects model, optimization of the ridge parameters and estimation of the regression parameters can be simultaneously executed. The linear structure of the varying coefficients then provides an asymptotic confidence interval as a function of location, but it is wider than a common pointwise confidence interval. We derive some tests for the varying coefficients and offer two examples using real data to illustrate our methodology. The results of the applied tests are summarized as the uniformity and the linearity of the varying coefficients.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"841 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":"116221244","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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