# KUBOKAWA, Tatsuya

## Curriculum Vitae

### Education

1987 | PhD. University of Tsukuba |

### Professional Experience

2001 | Professor, Faculty of Economics, University of Tokyo |

## Research Field

Mathematical Statistics

## Research Theme

In the field of statistical estimation, I have developed new theories to construct useful procedures which are more efficient than usual procedures such as unbiased or maximum likelihood estimators. For small sample, these usual procedures sometimes have drawbacks of instability or inefficiency. Also they sometimes take undesirable values beyond the parameter spaces. In the estimation problems with such undesirable properties, I have constructed classes of estimators which have uniformly smaller risks than usual estimators and eliminate their shortcoming. Out of the classes, I have singled out empirical Bayes and generalized Bayes estimators and other new and useful estimators. Especially I succeeded not only in establishing a new unified theory in the classical problem of estimating variance components in mixed linear models, but also in extending the theory to multivariate variance components models. Related to this multivariate extension, an innovative method for constructing minimax estimators of a covariance matrix was obtained in multivariate linear regression models.

## Publications

#### Articles - Publications after 2000

- T. Kubokawa and M.S. Srivastava (2001). Robust improvement in estimation of a mean matrix in an elliptically contoured distribution. Journal of Multivariate Analysis, 76, 138-152.
- T. Kubokawa and M.S. Srivastava (2002). Estimating risk and mean squared error matrix in Stein estimation. Journal of Multivariate Analysis, 82, 39-64.
- T. Kubokawa and M.S. Srivastava (2003). Estimating the covariance matrix: A new approach. Journal of Multivariate Analysis, 86, 28-47.
- T. Kubokawa and M.S. Srivastava (2003). Prediction in multivariate mixed linear models. Journal of the Japan Statistical Society, 33, 245-270.
- T. Kubokawa and M.S. Srivastava (2004). Improved empirical Bayes ridge regression estimators under multicollinearity. Communications in Statistics - Theory and Methods, 33, 1943-1973.
- T. Kubokawa (2004). Minimaxity in estimation of restricted parameters. Journal of the Japan Statistical Society, 34, No.2, 229-253.
- M.S. Srivastava and T. Kubokawa (2005). Minimax multivariate empirical Bayes estimators under multicollinearity. Journal of Multivariate Analysis, 93, 394-416.
- T. Kubokawa (2005). A revisit to estimation of the precision matrix of the Wishart distribution. Journal of Statistical Research, 39, No.1, 97-120. A special volume.
- Y. Sasase and T. Kubokawa (2005). Asymptotic correction of empirical Bayes confidence intervals and its application to small area estimation. Journal of the Japan Statistical Society, Series-J, 35, No.1, 27-54.
- T. Kubokawa (2005). Estimation of bounded location and scale parameters. Journal of the Japan Statistical Society, 35, No.2, 221-249.
- T. Kubokawa (2005). Estimation of a mean of a normal distribution with a bounded coefficient of variation. Sankhya, 67, Part 3, 499-525.
- T. Kubokawa (2006). Linear mixed models and small area estimation. Japanese Journal of Applied Statistics, 35, No.3, 139-161.
- T. Kubokawa and M.-T. Tsai (2006). Estimation of covariance matrices in fixed and mixed effects linear models. Journal of Multivariate Analysis, 97, Issue 10, 2242-2261.
- T. Kubokawa and W.E. Strawderman (2007). On minimaxity and admissibility of hierarchical Bayes estimators. Journal of Multivariate Analysis, 98, Issue 4, 829-851.
- M.-T. Tsai and T. Kubokawa (2007). Estimation of Wishart mean matrices under simple tree ordering. Journal of Multivariate Analysis, 98, Issue 5, 945-959.
- H. Tsukuma and T. Kubokawa (2007). Methods for improvement in estimation of a normal mean matrix. Journal of Multivariate Analysis, 98. Issue 8, 1592-1610.
- T. Kubokawa and H. Tsukuma (2007). Estimation in a linear regression model under the Kullback-Leibler loss and its application to model selection. Journal of Statistical Planning and Inference, 137, Issue 7, 2487-2508.
- M.S. Srivastava and T. Kubokawa (2007). Empirical Bayes regression analysis with many regressors but fewer observations. Journal of Statistical Planning and Inference, 137, Issue 11, 3778-3792.
- M.S. Srivastava and T. Kubokawa (2007). Comparison of discrimination methods for high dimensional data. Journal of the Japan Statistical Society, 37, No.1, 123-134.
- T. Kubokawa (2007). Characterization of priors in the Stein problem. Journal of the Japan Statistical Society, 37, No.2, 207-237.
- H. Tsukuma and T. Kubokawa (2007). Simultaneous estimation of normal precision matrices. Journal of Statistical Studies, 26, 119-138. A special volume in honor of the 75th birthday of Professor A.K.Md.E. Saleh.
- H. Tsukuma and T. Kubokawa (2008). Stein phenomenon in estimation of means restricted to a polyhedral convex cone. Journal of Multivariate Analysis, 99, Issue 1, 141-164.
- T. Kubokawa and M.S. Srivastava (2008). Estimation of the precision matrix of a singular Wishart distribution and its application in high dimensional data. Journal of Multivariate Analysis, 99, Issue 9, 1906-1928.
- M.S. Srivastava and T. Kubokawa (2008). Akaike information criterion for selecting components of the mean vector in high dimensional data with fewer observations. Journal of the Japan Statistical Society, 38, No.2, 259-283.
- T. Kubokawa (2008). Theory of linear mixed models and its applications to small area estimation. “Statistical Science in the 21st Century, III: Statistical Science in Mathematics and Computation”, (eds. G, Kitagawa and A. Takemura), 71-109, University of Tokyo Press.
- T. Kubokawa and H. Tsukuma (2008). Minimaxity of the Stein risk-minimization estimator for a normal mean matrix. Statistics and Decisions, 26, Issue 4, 243-261.
- H. Tsukuma and T. Kubokawa (2009). Minimax estimation of normal precisions via expansion estimators. Journal of Statistical Planning and Inference, 139, Issue 2, 295-309.
- T. Kubokawa (2009). Integral inequality for minimaxity in the Stein problem. Journal of the Japan Statistical Society, 39, No.2, 155-175.
- M.S. Srivastava and T. Kubokawa (2010). Conditional information criteria for selecting variables in linear mixed models. Journal of Multivariate Analysis, 101, 1970-1980.
- T. Kubokawa (2010). Corrected empirical Bayes confidence intervals in nested error regression models. Journal of the Korean Statistical Society, 39, No.2, 221-236.
- T. Kubokawa and Nyambaa Erdembat (2010). On testing linear hypothesis in a nested error regression model. Communication in Statistics - Theory and Methods, 39, 1552-1562. A special issue on “Recent Advances in Statistical Inference” in honor of retirements of Professor Masafumi Akahira.
- T. Kubokawa (2010). A review of linear mixed models and small area estimation. Journal of the Statistical Research, 44, No.1, 31-55.
- T. Kubokawa and M.S. Srivastava (2010). An empirical Bayes information criterion for selecting variables in linear mixed models. Journal of the Japan Statistical Society, 40, No.1, 111-130.
- Gauri S. Datta, T. Kubokawa, I. Molina and J. N. K. Rao (2011). Estimation of mean squared error of model-based small area estimators. Test, an Official Journal of the Spanish Society and Operations Research, 20, No.2, 367-388.
- T. Kubokawa and W.E. Strawderman (2011). Non-minimaxity of linear combinations of restricted location estimators and the related problems. Journal of Statistical Planning and Inference, 141, Issue 6, 2141-2155.
- H. Tsukuma and T. Kubokawa (2011). Modifying estimators of ordered positive parameters under the Stein loss. Journal of Multivariate Analysis, 102, Issue 1, 164-181.
- T. Kubokawa (2011). Conditional and unconditional methods for selecting variables in linear mixed models. Journal of Multivariate Analysis, 102, Issue 3, 641-660.
- T. Kubokawa and W.E. Strawderman (2011). A unified approach to non-minimaxity of sets of linear combinations of restricted location estimators. Journal of Multivariate Analysis, 102, Issue 10, 1429-1444.
- T. Kubokawa (2011). On measuring uncertainty of small area estimators with higher order accuracy. Journal of the Japan Statistical Society, 41, No.2, 93-119.
- T. Kubokawa (2012). Minimax estimation of linear combinations of restricted location parameters. “Contemporary Developments in Bayesian Analysis and Statistical Decision Theory: A Festschrift for William E. Strawderman”, IMS Collections, Vol. 8, 24-41, Institute of Mathematical Statistics.
- T. Kubokawa and B. Nagashima (2012). Parametric bootstrap methods for bias correction in linear mixed models. Journal of Multivariate Analysis, 106, 1-16.
- T. Kubokawa and M.S. Srivastava (2012). Selection of variables in multivariate regression models for large dimensions. Communications in Statistics - Theory and Methods, 41, Issue 13&14, 2465-2489.
- T. Kubokawa and M.S. Srivastava (2012). Akaike information criterion for selecting variables in a nested error regression model. Communications in Statistics - Theory and Methods, 41, Issue 15, 2626-2642.
- T. Kubokawa (2012). Estimation in restricted parameter space. (in Japanese) Journal of the Japan Statistical Society, J-Series 42, No.1, 153-176.
- M.S. Srivastava and T. Kubokawa (2013). Tests for multivariate analysis of variance in high dimension under non-normality. Journal of Multivariate Analysis, 115, 204-216.
- T. Kubokawa, M. Hyodo and M.S. Srivastava (2013). Asymptotic expansion and estimation of EPMC for linear classification rules in high dimension. Journal of Multivariate Analysis, 115, 496-515.
- T. Kubokawa, Eric Marchand, W.E. Strawderman and J.-P. Turcottex (2013). Minimaxity in predictive density estimation with parametric constraints. Journal of Multivariate Analysis, 116, 382-397.
- M. Kojima and T. Kubokawa (2013). Bartlett adjustments for hypotheses testing in linear models with general error covariance matrices. Journal of Multivariate Analysis, 122, 162-174.
- T. Kubokawa (2013). Constrained empirical Bayes estimator and its uncertainty in normal linear mixed models. Journal of Multivariate Analysis, 122, 377-392.
- T. Kubokawa and W.E. Strawderman (2013). Dominance properties of constrained Bayes and empirical Bayes estimators. Bernoulli, 19, Issue 5B, 2200-2221.
- T. Kubokawa, M. Hasukawa and K. Takahashi (2014). On measuring uncertainty of benchmarked predictors with application to disease risk estimate. Scandinavian Journal of Statistics, 41, 394-413.
- T. Kubokawa (2014). General dominance properties of double shrinkage estimators for ratio of positive parameters. Journal of Statistical Planning and Inference, 147, 224-234.
- T. Kubokawa and A. Inoue (2014). Estimation of covariance and precision matrices in high dimension. Electronic Journal of Statistics, 8, 130-158.
- M. Hyodo and T. Kubokawa (2014). A variable selection criterion for linear discriminant rule and its optimality in high dimensional and large sample setting. Journal of Multivariate Analysis, 123, 364-379.
- Y. Kawakubo and T. Kubokawa (2014). Modified conditional AIC in linear mixed models. Journal of Multivariate Analysis, 129, 44-56.
- M.S. Srivastava, H. Yanagihara and T. Kubokawa (2014). Tests for covariance matrices in high dimension with less sample size. Journal of Multivariate Analysis, 130, 289-309.
- T. Kubokawa, Eric Marchand and W.E. Strawderman (2014). On improved shrinkage estimators for concave loss. Statistics and Probability Letters, 96, 241-246.
- H. Tsukuma and T. Kubokawa (2015). Minimaxity in estimation of restricted and non-restricted scale parameter matrices. Annals of the Institute of Statistical Mathematics, 67, 261-285.
- S. Sugasawa and T. Kubokawa (2015). Parametric transformed Fay-Herriot model for small area estimation. Journal of Multivariate Analysis, 139, 295-311.
- H. Tsukuma and T. Kubokawa (2015). A unified approach to estimating a normal mean matrix in high and low dimensions. Journal of Multivariate Analysis, 139, 312-328.
- H. Tsukuma and T. Kubokawa (2015). Estimation of the mean vector in a singular multivariate normal distribution. Journal of Multivariate Analysis, 140, 245-258.
- T. Kubokawa, Eric Marchand and W.E. Strawderman (2015). On predictive density estimation for location families under integrated squared error loss. Journal of Multivariate Analysis, 142, 57-74.
- M. Ghosh, T. Kubokawa and Y. Kawakubo (2015). Benchmarked empirical Bayes methods in multiplicative area-level models with risk evaluation. Biometrika, 102, 647-659.
- T. Kubokawa, S. Sugasawa, M. Ghosh and S. Chaudhuri (2016). Prediction in heteroscedastic nested error regression models with random dispersions. Statistica Sinica, 26, 465-492.
- Y. Ikeda, T. Kubokawa and M.S. Srivastava (2016). Comparison of linear shrinkage estimators of a large covariance matrix in normal and non-normal distributions. Computational Statistics and Data Analysis, 95, 95-108.
- H. Tsukuma and T. Kubokawa (2016). Unified improvements in estimation of a normal covariance matrix in high and low dimensions. Journal of Multivariate Analysis, 143, 233-248.
- S. Sugasawa and T. Kubokawa (2016). On conditional prediction errors in mixed models with application to small area estimation. Journal of Multivariate Analysis, 148, 18-33.
- Y. Ikeda and T. Kubokawa (2016). Linear shrinkage estimation of large covariance matrices using factor models. Journal of Multivariate Analysis, 152, 61-81.
- T. Kubokawa (2016). Development of shrinkage methods in estimation - high dimensional analysis and small area estimation -. Journal of the Japan Statistical Society, J-Series, 46, No.1, 43-67.
- S. Sugasawa and T. Kubokawa (2017). Bayesian estimators in uncertain nested error regression models. Journal of Multivariate Analysis, 153, 52-63.
- S. Sugasawa, H. Tamae and T. Kubokawa (2017). Bayesian estimators for small area models shrinking both means and variances. Scandinavian Journal of Statistics, 44, 150-167.
- T. Kubokawa, Eric Marchand and W.E. Strawderman (2017). On predictive density estimation for location families under integrated absolute error loss. Bernoulli, 23, 3197-3212.
- H. Tsukuma and T. Kubokawa (2017). Proper Bayes and minimax predictive densities related to estimation of a normal mean matrix. Journal of Multivariate Analysis, 159, 138-150.
- S. Sugasawa and T. Kubokawa (2017). Transforming response values in small area prediction. Computational Statistics and Data Analysis, 114, 47-60.
- S. Sugasawa and T. Kubokawa (2017). Heteroscedastic nested error regression models with variance functions. Statistica Sinica, 27, 1101-1123.
- T. Kubokawa, E. Marchand and W.S. Strawderman (2017). A unified approach to estimation of noncentrality parameters, the multiple correlation coefficient, and mixture models. Mathematical Methods of Statistics, 26, 134-148.
- S. Sugasawa, T. Kubokawa and K. Ogasawara (2017). Empirical uncertain Bayes methods in area-level models. Scandinavian Journal of Statistics, 44, 684-706.
- S. Sugasawa, T. Kubokawa and J.N.K. Rao (2018). Small area estimation via unmatched sampling and linking models. Test, an Official Journal of the Spanish Society and Operations Research, 407-427.
- Y. Kawakubo, S. Sugasawa and T. Kubokawa (2018). Conditional Akaike information under covariate shift with application to small area estimation. Canadian Journal of Statistics, 46, 316-335.
- Y. Kawakubo, T. Kubokawa and M.S. Srivastava (2018). A variant of AIC based on the Bayesian marginal likelihood. Sankhya, Series B, 80, 60-84.
- R. Imai, T. Kubokawa and M. Ghosh (2018). Bayes minimax competitors of preliminary test estimators in k sample problems. Japanese Journal of Statistics and Data Science, 1, 3-21.
- M. Ghosh and T. Kubokawa (2018). Hierarchical empirical Bayes estimation of two sample means under divergence loss. Sankhya, 80-A, Supplement 1, S70-S83.
- R. Imai, T. Kubokawa and M. Ghosh (2019). Bayesian simultaneous estimation for means in k sample problems. Journal of Multivariate Analysis, 169, 49-60.
- Y. Hamura and T. Kubokawa (2019). Bayesian predictive distribution for a negative binomial model. Mathematical Methods of Statistics, 28, 1-17.
- S. Sugasawa, T. Kubokawa and J.N.K. Rao (2019). Hierarchical Bayes small area estimation with unknown link function. Scandinavian Journal of Statistics, 46, 885-897.
- T. Tsujino and T. Kubokawa (2019). Empirical Bayes methods in nested error regression models with skew-normal error. Japanese Journal of Statistics and Data Science, 2, 375-403.
- Y. Hamura and T. Kubokawa (2019). Simultaneous estimation of parameters of heterogeneous Poisson distributions. Japanese Journal of Statistics and Data Science, 2, 405-435.
- S. Sugasawa and T. Kubokawa (2019). Adaptively transformed mixed model prediction of general finite population parameters. Scandinavian Journal of Statistics, 46, 1025-1046.
- M. Ghosh and T. Kubokawa (2019). Hierarchical Bayes versus empirical Bayes density predictors under general divergence loss. Biometrika, 106, 495-500.
- H. Tsukuma and T. Kubokawa (2020). Estimation of a covariance matrix in multivariate skew-normal distribution. Communications in Statistics - Theory and Methods, 49, 1174-1200.
- T. Ghosh, M. Ghosh and T. Kubokawa (2020). On the loss robustness of least squares estimator. American Statisticians, 74, 64-67.
- T. Kubokawa, W.E. Strawderman and R. Yuasa (2020). Shrinkage estimation of location parameters in a multivariate skew-normal distribution. Communications in Statistics - Theory and Methods, 49, 2008-2024.
- Y. Hamura and T. Kubokawa (2020). Bayesian predictive distribution for a Poisson model with a parameter restriction. Communications in Statistics - Theory and Methods, 49, 3257-3266.
- T. Ito and T. Kubokawa (2020). Robust estimation of mean squared error matrix of small area estimators in a multivariate Fay-Herriot model. Japanese Journal of Statistics and Data Science, 3, 39-61.
- M. Ghosh, T. Kubokawa and G.S. Datta (2020). Density prediction and the Stein phenomenon. Sankhya, 82-A, 330-352.
- R. Yuasa and T. Kubokawa (2020). Ridge-type shrinkage estimation of the matrix mean of high-dimensional normal distribution. Journal of Multivariate Analysis, 178, 1-19.
- Y. Hamura and T. Kubokawa (2020). Bayesian shrinkage estimation of negative multinomial parameter vectors. Journal of Multivariate Analysis, 179, 1-22.
- Y. Hamura and T. Kubokawa (2020). Proper Bayes minimax estimation of parameters of Poisson distributions in the presence of unbalanced sample sizes. Brazilian Journal of Probability and Statistics, 34, 728-751.
- H. Tamae, K. Irie and T. Kubokawa (2020). A Score-adjusted approach to closed-form estimators for the gamma and beta distributions. Japanese Journal of Statistics and Data Science, 3, 543-561.
- S. Sugasawa and T. Kubokawa (2020). Small area estimation with mixed models : A review. Japanese Journal of Statistics and Data Science, 3, 693-720.
- T. Ito and T. Kubokawa (2021). Corrected empirical Bayes confidence region in a multivariate Fay-Herriot model. Journal of Statistical Planning and Inference, 211, 12-32.

#### Articles - Selected Publications before 2000

- T. Kubokawa (1987). Admissible minimax estimation of a common mean of two normal populations. The Annals of Statistics, 15, 1245-1256.
- P.K. Sen, T. Kubokawa and A.K.Md.E. Saleh (1989). The Stein paradox in the sense of the Pitman measure of closeness. The Annals of Statistics, 17, 1375-1386.
- T. Kubokawa (1991). An approach to improving the James-Stein estimator. Journal of Multivariate Analysis, 36, 121-126.
- T. Kubokawa, C. Robert and A.K.Md.E. Saleh (1992). Empirical Bayes estimation of the covariance matrix of a normal distribution with unknown mean under an entropy loss. Sankhya, Series A, 54, 402-410.
- T. Kubokawa (1994). A unified approach to improving equivariant estimators. The Annals of Statistics,22, 290-299.
- T. Kubokawa and C.P. Robert (1994). New perspectives on linear calibration. Journal of Multivariate Analysis, 51, 178-200.
- T. Kubokawa (1995). Estimation of variance components in mixed linear models. Journal of Multivariate Analysis, 53, 210-236.
- T. Kubokawa (1998). Double shrinkage estimation of common coefficients in two regression equations with heteroscedasticity. Journal of Multivariate Analysis, 67, 169-189.
- T. Kubokawa (1998). The Stein phenomenon in simultaneous estimation: A review. In: Applied Statistical Science III (eds. S.E. Ahmed, M. Ahsanullah and B.K. Sinha), 143-173, NOVA Science Publishers, Inc., New York. A special volume in honor of Professor A.K.Md.E. Saleh.
- T. Kubokawa (1999). Shrinkage and modification techniques in estimation of variance and the related problems: A review. Communication in Statistics - Theory and Methods, 28,613-650. A special issue on “Statistical Inference and Data Analysis” in honor of retirement of Professor Nariaki Sugiura.
- T. Kubokawa and M.S. Srivastava (1999). Robust improvement in estimation of a covariance matrix in an elliptically contoured distribution. The Annals of Statistics, 27, 600-609.
- M.S. Srivastava and T. Kubokawa (1999). Improved nonnegative estimation of multivariate components of variance. The Annals of Statistics, 27, 2008-2032.

#### Books and Monographs

- “Shrinkage Estimation for Mean and Covariance Matrices”, JSS Research Series in Statistics, Springer, 2020 (with Hisayuki Tsukuma)
- “Foundation of Modern Mathematical Statistics”, Kyouritsu Press, 2017
- “Statistics”, Tokyo University Press, 2016 (with Naoto Kunitomo)
- “Model Selection”, Iwanami Shoten Publishers, 2004 (with H. Shimodaira, H. Itoh and K. Takeuchi)

## Other Professional Activities and Awards

#### Other Professional Activities and Services

- “New development of shrinkage estimation methods in statistical inference”, JSPS Grant-in-Aid for Scientific Research, 18K11188, 2018-2022
- “Research on new developments of theory of statistical inference in several modern problems in multivariate analysis”, JSPS Grant-in-Aid for Scientific Research, 26330036, 2014-2018

#### Awards

- Japan Statistical Society Award 2015
- Japan Statistical Society Research Achievement Award 2011