The paper addresses the problem of selecting variables in linear mixed models (LMM). We propose the Empirical Bayes Information Criterion (EBIC) using a partial prior information on the parameters of interest. Specifically EBIC incorporates a non-subjective prior distribution on regression coefficients with an unknown hyper-parameter, but it is free from the setup of a prior information on the nuisance parameters like variance components. It is shown that EBIC not only has the nice asymptotic property of consistency as a variable selection, but also performs better in small and large sample sizes than the conventional methods like AIC, conditional AIC and BIC in light of selecting true variables.
{"title":"AN EMPIRICAL BAYES INFORMATION CRITERION FOR SELECTING VARIABLES IN LINEAR MIXED MODELS","authors":"T. Kubokawa, M. Srivastava","doi":"10.14490/JJSS.40.111","DOIUrl":"https://doi.org/10.14490/JJSS.40.111","url":null,"abstract":"The paper addresses the problem of selecting variables in linear mixed models (LMM). We propose the Empirical Bayes Information Criterion (EBIC) using a partial prior information on the parameters of interest. Specifically EBIC incorporates a non-subjective prior distribution on regression coefficients with an unknown hyper-parameter, but it is free from the setup of a prior information on the nuisance parameters like variance components. It is shown that EBIC not only has the nice asymptotic property of consistency as a variable selection, but also performs better in small and large sample sizes than the conventional methods like AIC, conditional AIC and BIC in light of selecting true variables.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"14 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126113955","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}
Let {Yn} be a sequence of nonnegative random variables (rvs), and Sn = ∑n j=1 Yj , n ≥ 1. It is first shown that independence of Sk−1 and Yk, for all 2 ≤ k ≤ n, does not imply the independence of Y1, Y2, . . . , Yn. When Yj ’s are identically distributed exponential Exp(α) variables, we show that the independence of Sk−1 and Yk, 2 ≤ k ≤ n, implies that the Sk follows a gamma G(α, k) distribution for every 1 ≤ k ≤ n. It is shown by a counterexample that the converse is not true. We show that if X is a non-negative integer valued rv, then there exists, under certain conditions, a rv Y ≥ 0 such that N(Y ) L = X, where {N(t)} is a standard (homogeneous) Poisson process, and obtain the Laplace-Stieltjes transform of Y . This leads to a new characterization for the gamma distribution. It is also shown that a G(α, k) distribution may arise as the distribution of Sk, where the components are not necessarily exponential. Several typical examples are discussed.
{"title":"Some Intrinsic Properties of the Gamma Distribution","authors":"P. Vellaisamy, M. Sreehari","doi":"10.14490/JJSS.40.133","DOIUrl":"https://doi.org/10.14490/JJSS.40.133","url":null,"abstract":"Let {Yn} be a sequence of nonnegative random variables (rvs), and Sn = ∑n j=1 Yj , n ≥ 1. It is first shown that independence of Sk−1 and Yk, for all 2 ≤ k ≤ n, does not imply the independence of Y1, Y2, . . . , Yn. When Yj ’s are identically distributed exponential Exp(α) variables, we show that the independence of Sk−1 and Yk, 2 ≤ k ≤ n, implies that the Sk follows a gamma G(α, k) distribution for every 1 ≤ k ≤ n. It is shown by a counterexample that the converse is not true. We show that if X is a non-negative integer valued rv, then there exists, under certain conditions, a rv Y ≥ 0 such that N(Y ) L = X, where {N(t)} is a standard (homogeneous) Poisson process, and obtain the Laplace-Stieltjes transform of Y . This leads to a new characterization for the gamma distribution. It is also shown that a G(α, k) distribution may arise as the distribution of Sk, where the components are not necessarily exponential. Several typical examples are discussed.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"13 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"122169283","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}
K. Yamamoto, Kouji Tahata, Asuka Hatori, S. Tomizawa
For multi-way tables with ordered categories, Tahata et al. (2008) considered the collapsed symmetry model, which indicates the symmetry for the tables collapsed the original table by choosing the cut point in the categories. The present paper proposes a measure to represent the degree of departure from collapsed symmetry for multi-way tables. The measure proposed is expressed by using the Cressie-Read power-divergence or the Patil-Taillie diversity index. The measure would be useful for comparing the degrees of departure from collapsed symmetry in several multi-way tables. Examples are given.
{"title":"MEASURE OF DEPARTURE FROM COLLAPSED SYMMETRY FOR MULTI-WAY CONTINGENCY TABLES WITH ORDERED CATEGORIES","authors":"K. Yamamoto, Kouji Tahata, Asuka Hatori, S. Tomizawa","doi":"10.14490/JJSS.40.097","DOIUrl":"https://doi.org/10.14490/JJSS.40.097","url":null,"abstract":"For multi-way tables with ordered categories, Tahata et al. (2008) considered the collapsed symmetry model, which indicates the symmetry for the tables collapsed the original table by choosing the cut point in the categories. The present paper proposes a measure to represent the degree of departure from collapsed symmetry for multi-way tables. The measure proposed is expressed by using the Cressie-Read power-divergence or the Patil-Taillie diversity index. The measure would be useful for comparing the degrees of departure from collapsed symmetry in several multi-way tables. Examples are given.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"25 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"116738480","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 talk, we consider profile analysis of several groups where the groups have partly equal means. This leads to a profile analysis for a growth curve model. The likelihood ratio statistics are ...
{"title":"Profile Analysis for a Growth Curve Model","authors":"Martin Ohlson, M. Srivastava","doi":"10.14490/JJSS.40.001","DOIUrl":"https://doi.org/10.14490/JJSS.40.001","url":null,"abstract":"In this talk, we consider profile analysis of several groups where the groups have partly equal means. This leads to a profile analysis for a growth curve model. The likelihood ratio statistics are ...","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"38 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"124512455","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, a modified inverse stereographic projection, from the real line to the circle, is used as the motivation for a means of resolving a discontinuity in the Minh–Farnum family of circular distributions. A four-parameter family of symmetric unimodal distributions which extends both the Minh–Farnum and Jones–Pewsey families is proposed. The normalizing constant of the density can be expressed in terms of Appell’s function or, equivalently, the Gauss hypergeometric function. Important special cases of the family are identified, expressions for its trigonometric moments are obtained, and methods for simulating random variates from it are described. Parameter estimation based on method of moments and maximum likelihood techniques is discussed, and the latter approach is used to fit the family of distributions to an illustrative data set. A further extension to a family of rotationally symmetric distributions on the sphere is briefly made.
{"title":"Symmetric Unimodal Models for Directional Data Motivated by Inverse Stereographic Projection","authors":"Toshihiro Abe, K. Shimizu, A. Pewsey","doi":"10.14490/JJSS.40.045","DOIUrl":"https://doi.org/10.14490/JJSS.40.045","url":null,"abstract":"In this paper, a modified inverse stereographic projection, from the real line to the circle, is used as the motivation for a means of resolving a discontinuity in the Minh–Farnum family of circular distributions. A four-parameter family of symmetric unimodal distributions which extends both the Minh–Farnum and Jones–Pewsey families is proposed. The normalizing constant of the density can be expressed in terms of Appell’s function or, equivalently, the Gauss hypergeometric function. Important special cases of the family are identified, expressions for its trigonometric moments are obtained, and methods for simulating random variates from it are described. Parameter estimation based on method of moments and maximum likelihood techniques is discussed, and the latter approach is used to fit the family of distributions to an illustrative data set. A further extension to a family of rotationally symmetric distributions on the sphere is briefly made.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"15 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131604927","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}
Takayuki Shiohama, M. Hallin, David Veredas, M. Taniguchi
We model large panels of financial time series by means of generalized dynamic factor models with multivariate GARCH idiosyncratic components. Such models combine the features of dynamic factors with those of a generalized smooth transition conditional correlation (GSTCC) model, which belongs to the class of time-varying conditional correlation models. The model is applied to dynamic portfolio allocation with Value at Risk constraints on 6.5 years of daily TOPIX Sector Indexes. Results show that the proposed model yields better portfolio performance than other multivariate models proposed in the literature, including the traditional mean-variance approach.
{"title":"DYNAMIC PORTFOLIO OPTIMIZATION USING GENERALIZED DYNAMIC CONDITIONAL HETEROSKEDASTIC FACTOR MODELS","authors":"Takayuki Shiohama, M. Hallin, David Veredas, M. Taniguchi","doi":"10.14490/JJSS.40.145","DOIUrl":"https://doi.org/10.14490/JJSS.40.145","url":null,"abstract":"We model large panels of financial time series by means of generalized dynamic factor models with multivariate GARCH idiosyncratic components. Such models combine the features of dynamic factors with those of a generalized smooth transition conditional correlation (GSTCC) model, which belongs to the class of time-varying conditional correlation models. The model is applied to dynamic portfolio allocation with Value at Risk constraints on 6.5 years of daily TOPIX Sector Indexes. Results show that the proposed model yields better portfolio performance than other multivariate models proposed in the literature, including the traditional mean-variance approach.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"47 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"123691252","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 class of curved exponential families whose likelihood function admits the conjugate analysis is derived, and its duality is explored. We show that conjugacy yields the existence of sufficient statistics as well as duality. Extended versions of the mean and the canonical parameters can be defined, which shed a new light on duality and the conjugate analysis in the exponential family. As a result, an essential reason is revealed as to why a common prior density can be conjugate for different sampling densities, as in the case of a gamma prior density which is conjugate for the Poisson and the gamma sampling densities. The least information property of the conjugate analysis is explained, which is compatible with the minimax property of the generalized linear model. We also derive dual Pythagorean relationships with respect to posterior risks to show the optimality of the Bayes estimator.
{"title":"Duality Induced from Conjugacy in the Curved Exponential Family","authors":"Toshio Ohnishi, T. Yanagimoto","doi":"10.14490/JJSS.40.023","DOIUrl":"https://doi.org/10.14490/JJSS.40.023","url":null,"abstract":"A class of curved exponential families whose likelihood function admits the conjugate analysis is derived, and its duality is explored. We show that conjugacy yields the existence of sufficient statistics as well as duality. Extended versions of the mean and the canonical parameters can be defined, which shed a new light on duality and the conjugate analysis in the exponential family. As a result, an essential reason is revealed as to why a common prior density can be conjugate for different sampling densities, as in the case of a gamma prior density which is conjugate for the Poisson and the gamma sampling densities. The least information property of the conjugate analysis is explained, which is compatible with the minimax property of the generalized linear model. We also derive dual Pythagorean relationships with respect to posterior risks to show the optimality of the Bayes estimator.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"167 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-11-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"121897574","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}
Junichi Hirukawa, Hiroyuki Taniai, M. Hallin, M. Taniguchi
The portfolio of the Japanese Government Pension Investment Fund (GPIF) consists of a linear combination of five benchmarks of financial assets. Some of these exhibit long-memory and nonlinear behavior. Their analysis therefore requires multivariate nonlinear and long-memory time series models. Moreover, the assumption that the innovation densities underlying those models are known seems quite unrealistic. If those densities remain unspecified, the model becomes a semiparametric one, and rank-based inference methods naturally come into the picture. Rank-based inference methods under very general conditions are known to achieve the semiparametric efficiency bounds. Defining ranks in the context of multivariate time series models, however, is not obvious. We propose two distinct definitions. The first one relies on the assumption that the innovation density is some unspecified elliptical density. The second one relies on the assumption that the innovation process is described by some unspecified independent component analysis model. Applications to portfolio management problems are discussed.
{"title":"Rank-based Inference for Multivariate Nonlinear and Long-memory Time Series Models","authors":"Junichi Hirukawa, Hiroyuki Taniai, M. Hallin, M. Taniguchi","doi":"10.14490/JJSS.40.167","DOIUrl":"https://doi.org/10.14490/JJSS.40.167","url":null,"abstract":"The portfolio of the Japanese Government Pension Investment Fund (GPIF) consists of a linear combination of five benchmarks of financial assets. Some of these exhibit long-memory and nonlinear behavior. Their analysis therefore requires multivariate nonlinear and long-memory time series models. Moreover, the assumption that the innovation densities underlying those models are known seems quite unrealistic. If those densities remain unspecified, the model becomes a semiparametric one, and rank-based inference methods naturally come into the picture. Rank-based inference methods under very general conditions are known to achieve the semiparametric efficiency bounds. Defining ranks in the context of multivariate time series models, however, is not obvious. We propose two distinct definitions. The first one relies on the assumption that the innovation density is some unspecified elliptical density. The second one relies on the assumption that the innovation process is described by some unspecified independent component analysis model. Applications to portfolio management problems are discussed.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"27 15_suppl 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"126913424","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}
Parametric estimation of cause-specific hazard functions in a competing risks model is considered. An approximate likelihood procedure for estimating parameters of cause-specific hazard functions based on competing risks data subject to right censoring is proposed. In an assumed parametric model that may have been misspecified, an estimator of a parameter is said to be consistent if it converges in probability to the pseudo-true value of the parameter as the sample size becomes large. Under censorship, the ordinary maximum likelihood method does not necessarily give consistent estimators. The proposed approximate likelihood procedure is consistent even if the parametric model is misspecified. An asymptotic distribution of the approximate maximum likelihood estimator is obtained, and the efficiency of the estimator is discussed. Datasets from a simulation experiment, an electrical appliance test and a pneumatic tire test are used to illustrate the procedure.
{"title":"An Approximate Likelihood Procedure for Competing Risks Data","authors":"A. Suzukawa","doi":"10.14490/JJSS.40.239","DOIUrl":"https://doi.org/10.14490/JJSS.40.239","url":null,"abstract":"Parametric estimation of cause-specific hazard functions in a competing risks model is considered. An approximate likelihood procedure for estimating parameters of cause-specific hazard functions based on competing risks data subject to right censoring is proposed. In an assumed parametric model that may have been misspecified, an estimator of a parameter is said to be consistent if it converges in probability to the pseudo-true value of the parameter as the sample size becomes large. Under censorship, the ordinary maximum likelihood method does not necessarily give consistent estimators. The proposed approximate likelihood procedure is consistent even if the parametric model is misspecified. An asymptotic distribution of the approximate maximum likelihood estimator is obtained, and the efficiency of the estimator is discussed. Datasets from a simulation experiment, an electrical appliance test and a pneumatic tire test are used to illustrate the procedure.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"40 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"130605337","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 discusses resampling procedures in the estimation of optimal portfolios when the returns are VAR( p ) processes and VGARCH( p, q ) processes. Then a consistency between the estimation error of the estimator of the mean-variance optimal portfolio parameter and that of the resampled one is shown. Based on this we construct an estimator of the lower tail of the estimation error. Moreover, we introduce the Estimation Error Efficient Portfolio which considers the estimation error as the portfolio risk. Numerical results show that our approach is applicable to actual portfolio management.
{"title":"Resampling Procedure to Construct Estimation Error Efficient Portfolios for Stationary Returns of Assets","authors":"Hiroshi Shiraishi","doi":"10.14490/JJSS.40.189","DOIUrl":"https://doi.org/10.14490/JJSS.40.189","url":null,"abstract":"This paper discusses resampling procedures in the estimation of optimal portfolios when the returns are VAR( p ) processes and VGARCH( p, q ) processes. Then a consistency between the estimation error of the estimator of the mean-variance optimal portfolio parameter and that of the resampled one is shown. Based on this we construct an estimator of the lower tail of the estimation error. Moreover, we introduce the Estimation Error Efficient Portfolio which considers the estimation error as the portfolio risk. Numerical results show that our approach is applicable to actual portfolio management.","PeriodicalId":326924,"journal":{"name":"Journal of the Japan Statistical Society. Japanese issue","volume":"45 1","pages":"0"},"PeriodicalIF":0.0,"publicationDate":"2010-03-22","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"131134070","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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