We consider a fractional 212 factorial design derived from a simple partially balanced array (SPBA), and we assume that the non-negligible factorial effects are the general mean, all the main effects and the two-factor interactions between the m1 factors and the m2 ones, and mk ≥ 2 (k = 1, 2). In this paper, we give a necessary and sufficient condition for an SPBA to be a partially balanced fractional 212 factorial design such that all the non-negligible factorial effects are estimable, whose design is said to be of resolution R({00, 10, 01, 11}). Such a design is concretely characterized by the suffixes of the indices of an SPBA.
{"title":"Characterization of Partially Balanced Fractional 2m1+m2 Factorial Designs of Resolution R({00, 10, 01, 11})","authors":"Hiromu Yumiba, Y. Hyodo, M. Kuwada","doi":"10.14490/JJSS.42.47","DOIUrl":"https://doi.org/10.14490/JJSS.42.47","url":null,"abstract":"We consider a fractional 212 factorial design derived from a simple partially balanced array (SPBA), and we assume that the non-negligible factorial effects are the general mean, all the main effects and the two-factor interactions between the m1 factors and the m2 ones, and mk ≥ 2 (k = 1, 2). In this paper, we give a necessary and sufficient condition for an SPBA to be a partially balanced fractional 212 factorial design such that all the non-negligible factorial effects are estimable, whose design is said to be of resolution R({00, 10, 01, 11}). Such a design is concretely characterized by the suffixes of the indices of an SPBA.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"19 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126928539","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 method of probability generating functions is extended for obtaining exact distributions of the number of occurrences of a discrete pattern in undirected graphical models. General results for deriving the distributions are given with illustrative examples. Further, a device for reducing calculations is proposed. It works effectively when the graphical model is relatively simple. An algorithm for obtaining the distributions including the device is also given. In order to show the feasibility of our method, exact distributions of the number of occurrences of a “1”-run are derived in two undirected graphical models whose vertices are allocated on a sphere and a torus, respectively. As an application of our results, the exact reliabilities of consecutive-k-out-of-n:F systems corresponding to the undirected graphical models are obtained.
{"title":"Exact Distributions of the Number of Pattern Occurrences in Undirected Graphical Models","authors":"S. Aki, K. Inoue","doi":"10.14490/JJSS.42.59","DOIUrl":"https://doi.org/10.14490/JJSS.42.59","url":null,"abstract":"The method of probability generating functions is extended for obtaining exact distributions of the number of occurrences of a discrete pattern in undirected graphical models. General results for deriving the distributions are given with illustrative examples. Further, a device for reducing calculations is proposed. It works effectively when the graphical model is relatively simple. An algorithm for obtaining the distributions including the device is also given. In order to show the feasibility of our method, exact distributions of the number of occurrences of a “1”-run are derived in two undirected graphical models whose vertices are allocated on a sphere and a torus, respectively. As an application of our results, the exact reliabilities of consecutive-k-out-of-n:F systems corresponding to the undirected graphical models are obtained.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"1 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-09-04","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130483882","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 propose semiparametric estimation of the memory parameter that controls persistence of autocorrelation in stationary long-memory signal plus white noise processes, including an important extension to long-memory stochastic volatility (LMSV) models. The proposed estimation is constructed from the Whittle likelihood based on fractional exponential (FEXP) models, which is called a global or broadband semiparametric estimation. We establish that the estimators are consistent without Gaussianity. A numerical examination reveals that the proposed estimation works well in finite samples. Finally, we provide an illustrative example of volatility analysis by using the LMSV model.
{"title":"Global Semiparametric Estimation of Long-memory Signal Plus Noise Processes","authors":"M. Narukawa","doi":"10.14490/JJSS.41.205","DOIUrl":"https://doi.org/10.14490/JJSS.41.205","url":null,"abstract":"We propose semiparametric estimation of the memory parameter that controls persistence of autocorrelation in stationary long-memory signal plus white noise processes, including an important extension to long-memory stochastic volatility (LMSV) models. The proposed estimation is constructed from the Whittle likelihood based on fractional exponential (FEXP) models, which is called a global or broadband semiparametric estimation. We establish that the estimators are consistent without Gaussianity. A numerical examination reveals that the proposed estimation works well in finite samples. Finally, we provide an illustrative example of volatility analysis by using the LMSV model.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"41 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"115179130","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}
Zografos et al. (1990) introduced the φ-divergence family of statistics Cφ to the goodness-of-fit test. The φ-divergence family of statistics Cφ includes the power divergence family of statistics proposed by Cressie and Read (Cressie and Read (1984) and Read and Cressie (1988)) as a special case. Sekiya and Taneichi (2004) derived the multivariate Edgeworth expansion assuming a continuous distribution for the distributions of power divergence statistics under a nonlocal alternative hypothesis. In this paper, we consider an expansion for the family of general φ-divergence statistics Cφ. We derive the multivariate Edgeworth expansion assuming a continuous distribution for the distribution of Cφ under a nonlocal alternative hypothesis. By using the expansion, we propose a new approximation for the power of the statistic Cφ. We numerically investigate the accuracy of the approximation when two types of concrete φ-divergence statistics are applied. By the numerical investigation, we show that the present approximation is a good approximation especially when alternative hypotheses are distant from the null hypothesis.
Zografos et al.(1990)将φ-散度统计量Cφ引入到拟合优度检验中。φ-散度统计族Cφ包括Cressie和Read (Cressie and Read(1984)和Read and Cressie(1988))提出的幂散度统计族作为特例。Sekiya和Taneichi(2004)对非局部可选假设下的功率散度统计分布，导出了假设连续分布的多元Edgeworth展开式。本文考虑一般φ-散度统计量Cφ族的展开式。在非局部备择假设下，我们导出了Cφ分布在连续分布下的多元Edgeworth展开式。利用展开式，我们提出了统计量Cφ幂的一个新的近似。用数值方法研究了两类混凝土φ散度统计量的近似精度。通过数值研究，我们表明，目前的近似是一个很好的近似，特别是当备选假设远离零假设。
{"title":"Improved Approximations for the Distributions of Multinomial Goodness-of-fit Statistics Based on φ-divergence under Nonlocal Alternatives","authors":"P. Htwe, N. Taneichi, Y. Sekiya","doi":"10.14490/JJSS.41.121","DOIUrl":"https://doi.org/10.14490/JJSS.41.121","url":null,"abstract":"Zografos et al. (1990) introduced the φ-divergence family of statistics Cφ to the goodness-of-fit test. The φ-divergence family of statistics Cφ includes the power divergence family of statistics proposed by Cressie and Read (Cressie and Read (1984) and Read and Cressie (1988)) as a special case. Sekiya and Taneichi (2004) derived the multivariate Edgeworth expansion assuming a continuous distribution for the distributions of power divergence statistics under a nonlocal alternative hypothesis. In this paper, we consider an expansion for the family of general φ-divergence statistics Cφ. We derive the multivariate Edgeworth expansion assuming a continuous distribution for the distribution of Cφ under a nonlocal alternative hypothesis. By using the expansion, we propose a new approximation for the power of the statistic Cφ. We numerically investigate the accuracy of the approximation when two types of concrete φ-divergence statistics are applied. By the numerical investigation, we show that the present approximation is a good approximation especially when alternative hypotheses are distant from the null hypothesis.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128539570","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}
Computationally efficient methods for Bayesian analysis of Seemingly Unrelated Regression (SUR) models with a large number of predictors are developed. One of the most crucial problems in Bayesian modeling of SUR models is how to determine the optimal combination of predictors. In this paper, under a Bayesian hierarchical framework where each regression function is represented as a linear combination of a large number of basis functions, the regression coefficients, the variance matrix of the errors, and a set of predictors to be included in the model are estimated simultaneously. Usually the Bayesian model estimation problem is solved using Markov Chain Monte Carlo (MCMC) techniques. Herein we show how a direct Monte Carlo (DMC) technique can be employed to solve the variable selection and model parameter estimation problems more efficiently.
{"title":"Bayesian Variable Selection for the Seemingly Unrelated Regression Models with a Large Number of Predictors","authors":"T. Ando","doi":"10.14490/JJSS.41.187","DOIUrl":"https://doi.org/10.14490/JJSS.41.187","url":null,"abstract":"Computationally efficient methods for Bayesian analysis of Seemingly Unrelated Regression (SUR) models with a large number of predictors are developed. One of the most crucial problems in Bayesian modeling of SUR models is how to determine the optimal combination of predictors. In this paper, under a Bayesian hierarchical framework where each regression function is represented as a linear combination of a large number of basis functions, the regression coefficients, the variance matrix of the errors, and a set of predictors to be included in the model are estimated simultaneously. Usually the Bayesian model estimation problem is solved using Markov Chain Monte Carlo (MCMC) techniques. Herein we show how a direct Monte Carlo (DMC) technique can be employed to solve the variable selection and model parameter estimation problems more efficiently.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"33 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2012-02-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126222693","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}
Cataract surgery results when a patient decides to undergo lens surgery following a diagnosis of a clinically significant cataract (CSC). Because the presence of a CSC is generally latent and unobserved, a person might not receive cataract surgery even if the person has a CSC. This misclassification needs to be adjusted in the statistical analysis of CSC so as to reduce the bias in the parameter estimation. Following Magder and Hughes (1997) and using the cataract surgery data on atomic-bomb survivors at the Radiation Effects Research Foundation, we used this method for estimating the prevalence of CSC in a linear logistic dose response model taking account of the sensitivity and/or specificity of the decision for lens surgery. The estimated sensitivity was 0.385 (95% CI: 0.268, 0.517) and the estimated specificity was perfect. The odds ratio estimate for the radiation dose response changed from 1.39 (95% CI: 1.24, 1.55) to 1.58 (95% CI: 1.26, 1.98) when allowing for the imperfect sensitivity. A large sample simulation study with a continuous covariate was conducted, assuming either imperfect sensitivity or imperfect specificity, to investigate the performance of the method. Results indicated that the parameter estimates are almost correct. We calculated the asymptotic relative efficiency (ARE) for a simple logistic regression slope estimate and showed that the ARE depends only on the values of slope and intercept parameters.
{"title":"Assessment of Misclassification in a Binary Response: Recovering Information on Clinically Significant Cataract Prevalence from Cataract Surgery Data in Atomic-bomb Survivors","authors":"E. Nakashima, Y. Fujii, K. Neriishi, A. Minamoto","doi":"10.14490/JJSS.41.017","DOIUrl":"https://doi.org/10.14490/JJSS.41.017","url":null,"abstract":"Cataract surgery results when a patient decides to undergo lens surgery following a diagnosis of a clinically significant cataract (CSC). Because the presence of a CSC is generally latent and unobserved, a person might not receive cataract surgery even if the person has a CSC. This misclassification needs to be adjusted in the statistical analysis of CSC so as to reduce the bias in the parameter estimation. Following Magder and Hughes (1997) and using the cataract surgery data on atomic-bomb survivors at the Radiation Effects Research Foundation, we used this method for estimating the prevalence of CSC in a linear logistic dose response model taking account of the sensitivity and/or specificity of the decision for lens surgery. The estimated sensitivity was 0.385 (95% CI: 0.268, 0.517) and the estimated specificity was perfect. The odds ratio estimate for the radiation dose response changed from 1.39 (95% CI: 1.24, 1.55) to 1.58 (95% CI: 1.26, 1.98) when allowing for the imperfect sensitivity. A large sample simulation study with a continuous covariate was conducted, assuming either imperfect sensitivity or imperfect specificity, to investigate the performance of the method. Results indicated that the parameter estimates are almost correct. We calculated the asymptotic relative efficiency (ARE) for a simple logistic regression slope estimate and showed that the ARE depends only on the values of slope and intercept parameters.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"6 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"114192855","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 consider kernel-based estimators in the nonparametric binary regression problem with multidimensional covariates. We propose a local linear type estimator of the response probability function with kernel weighted at each observed covariate. In addition, we discuss the rule of thumb bandwidth selector and the plug-in bandwidth selector. The efficiency of the weighted local linear estimator is determined from results of asymptotic properties and our simulation study.
{"title":"KERNEL BINARY REGRESSION WITH MULTIPLE COVARIATES","authors":"Hidenori Okumura","doi":"10.14490/JJSS.41.001","DOIUrl":"https://doi.org/10.14490/JJSS.41.001","url":null,"abstract":"In this paper, we consider kernel-based estimators in the nonparametric binary regression problem with multidimensional covariates. We propose a local linear type estimator of the response probability function with kernel weighted at each observed covariate. In addition, we discuss the rule of thumb bandwidth selector and the plug-in bandwidth selector. The efficiency of the weighted local linear estimator is determined from results of asymptotic properties and our simulation study.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"39 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"128845626","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}
Consider a sequence of independent observations X1, . . . , Xn from a N(θ, cθ) distribution with 0 0) is known. We begin with the problem of testing H0 : θ = θ0 against H1 : θ = θ1 where θ0, θ1(θ0 = θ1) are specified values of θ. The most powerful (MP) level α test depends upon ∑n i=1 X 2 i , a complete and sufficient statistic for θ, which has a multiple of a non-central chi-square distribution with its non-centrality parameter involving n and the true parameter value θ under H0, H1. We first target type-I and type-II error probabilities α and β respectively, with α > 0, β > 0, α + β < 1. We set out to determine the required exact sample size which will control these error probabilities and provide two useful large-sample approximations for the sample size. The three methods provide nearly the same required sample size whether n is small, moderate or large. We also show how one may derive the minimum variance unbiased estimators (MVUEs) for a number of interesting and useful functionals of θ by combining some previous work from Mukhopadhyay and Cicconetti (2004) and Mukhopadhyay and Bhattacharjee (2010). All methodologies are illustrated with both simulated data and real data.
{"title":"ON MP TEST AND THE MVUEs IN A N (θ,cθ) DISTRIBUTION WITH θ UNKNOWN : ILLUSTRATIONS AND APPLICATIONS","authors":"D. Bhattacharjee, N. Mukhopadhyay","doi":"10.14490/JJSS.41.075","DOIUrl":"https://doi.org/10.14490/JJSS.41.075","url":null,"abstract":"Consider a sequence of independent observations X1, . . . , Xn from a N(θ, cθ) distribution with 0 0) is known. We begin with the problem of testing H0 : θ = θ0 against H1 : θ = θ1 where θ0, θ1(θ0 = θ1) are specified values of θ. The most powerful (MP) level α test depends upon ∑n i=1 X 2 i , a complete and sufficient statistic for θ, which has a multiple of a non-central chi-square distribution with its non-centrality parameter involving n and the true parameter value θ under H0, H1. We first target type-I and type-II error probabilities α and β respectively, with α > 0, β > 0, α + β < 1. We set out to determine the required exact sample size which will control these error probabilities and provide two useful large-sample approximations for the sample size. The three methods provide nearly the same required sample size whether n is small, moderate or large. We also show how one may derive the minimum variance unbiased estimators (MVUEs) for a number of interesting and useful functionals of θ by combining some previous work from Mukhopadhyay and Cicconetti (2004) and Mukhopadhyay and Bhattacharjee (2010). All methodologies are illustrated with both simulated data and real data.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"44 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124495717","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 k-sample and change point problems for independent data in a unified way. We propose a test statistic based on the rank statisitcs. The asymptotic distribution under the null hypothesis is shown to be the supremum of the 2-dimensional standard Brownian pillow. Also, the test is shown to be consistent under the alternative that k distribution functions are linearly independent. It is important from practical point of view that our test is not only asymptotically distribution free but also distribution free even for fixed finite sample.
{"title":"A Rank Statistic for Non-parametric k -sample and Change Point Problems","authors":"Y. Nishiyama","doi":"10.14490/JJSS.41.067","DOIUrl":"https://doi.org/10.14490/JJSS.41.067","url":null,"abstract":"We consider k-sample and change point problems for independent data in a unified way. We propose a test statistic based on the rank statisitcs. The asymptotic distribution under the null hypothesis is shown to be the supremum of the 2-dimensional standard Brownian pillow. Also, the test is shown to be consistent under the alternative that k distribution functions are linearly independent. It is important from practical point of view that our test is not only asymptotically distribution free but also distribution free even for fixed finite sample.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-08-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121663372","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 is concerned with asymptotic theory for penalized spline estimator in bivariate additive model. The focus of this paper is put upon the penalized spline estimator obtained by the backfitting algorithm. The convergence of the algorithm as well as the uniqueness of its solution are shown. The asymptotic bias and variance of penalized spline estimator are derived by an efficient use of the asymptotic results for the penalized spline estimator in marginal univariate model. Asymptotic normality of estimator is also developed, by which an approximate confidence interval can be obtained. Some numerical experiments confirming theoretical results are provided.
{"title":"ASYMPTOTICS FOR PENALIZED ADDITIVE B-SPLINE REGRESSION","authors":"Takuma Yoshida, Kanta Naito","doi":"10.14490/JJSS.42.81","DOIUrl":"https://doi.org/10.14490/JJSS.42.81","url":null,"abstract":"This paper is concerned with asymptotic theory for penalized spline estimator in bivariate additive model. The focus of this paper is put upon the penalized spline estimator obtained by the backfitting algorithm. The convergence of the algorithm as well as the uniqueness of its solution are shown. The asymptotic bias and variance of penalized spline estimator are derived by an efficient use of the asymptotic results for the penalized spline estimator in marginal univariate model. Asymptotic normality of estimator is also developed, by which an approximate confidence interval can be obtained. Some numerical experiments confirming theoretical results are provided.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"62 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2011-04-27","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"133777732","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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