## Basic Information

### Academic Degrees

- Doctor of Science, Hiroshima University
- Master of Science, Hiroshima University

### Research Fields

- Informatics;Principles of Informatics;Statistical science

### Research Keywords

- High-dimension
- non-normal populations
- irregular models
- Discrimination
- Asymptotics
- Two stage sampling

## Educational Activity

### Course in Charge

- 2023, Liberal Arts Education Program1, 4Term, Fundamental Data Science
- 2023, Undergraduate Education, Intensive, Basic mathematics
- 2023, Undergraduate Education, 3Term, Probability and Mathematical Statistics B
- 2023, Undergraduate Education, First Semester, Special Study of Mathematics and Informatics for Graduation
- 2023, Undergraduate Education, Second Semester, Special Study of Mathematics and Informatics for Graduation
- 2023, Undergraduate Education, 2Term, Nonparametric analysis
- 2023, Graduate Education (Master's Program) , 2Term, Mathematical Omnibus
- 2023, Graduate Education (Master's Program) , Academic Year, Mathematical Statistics Seminar
- 2023, Graduate Education (Master's Program) , Academic Year, Mathematical Statistics Seminar
- 2023, Graduate Education (Master's Program) , 1Term, Probability and Mathematical Statistics D
- 2023, Graduate Education (Master's Program) , 4Term, Topics in Probability and Mathematical Statistics D
- 2023, Graduate Education (Master's Program) , Academic Year, Exercises in Mathematics
- 2023, Graduate Education (Master's Program) , First Semester, Exercises in Mathematics A
- 2023, Graduate Education (Master's Program) , Second Semester, Exercises in Mathematics B
- 2023, Graduate Education (Master's Program) , Academic Year, Seminar in Mathematics
- 2023, Graduate Education (Doctoral Program) , Academic Year, Seminar in Mathematics

## Research Activities

### Academic Papers

- Laplace expansion for Bartlett--Nanda--Pillai's test statistic and its error bound, Teor. Veroyatnost. i Primenen, 68(4), 705-718, 2023
- Optimization of generalized Cp criterion for selecting ridge parameters in generalized ridge regression., Intelligent Decision Technologies 2020, Proceedings of the 12th KES Interna tional Conference on Intelligent Decision Technologies (KES-IDT-20) (eds. I. Czarnowski, R. J. Howlett & L. C. Jain), 267-278, Springer., 2020
- Principalcomponents regression by using generalized principal components analysis., J. Japan Statist. Soc., 43(1), 57-78, 2013
- Optimization of generalized C p criterion for selecting ridge parameters in generalized ridge regression, Intelligent Decision Technologies 2020, Proceedings of the 12th KES Interna- tional Conference on Intelligent Decision Technologies (KES-IDT-20) (eds. I. Czarnowski, R. J. Howlett & L. C. Jain), 267-278, 2020
- COMPUTABLE ERROR BOUNDS FOR HIGH-DIMENSIONAL APPROXIMATIONS OF AN LR STATISTIC FOR ADDITIONAL INFORMATION IN CANONICAL CORRELATION ANALYSIS, THEORY OF PROBABILITY AND ITS APPLICATIONS, 62(1), 157-172, 2018
- EPMC estimation in discriminant analysis when the dimension and sample sizes are large, HIROSHIMA MATHEMATICAL JOURNAL, 47(1), 43-62, 201703
- Selection of the linear and quadratic discriminant functions when the difference between two covariance matrices are small, J. Japan Statist. Soc., 47(2), 145-165, 2017
- Asymptotic expansions of the null distribution of the LR test statistic for random-effects covariance structure in a parallel profile model, Journal of the Japan Statistical Society, 46(1), 51-79, 201606
- ★, A consistency property of the AIC for multivariate linear models when the dimension and the sample size are large, ELECTRONIC JOURNAL OF STATISTICS, 9(1), 869-897, 2015
- Simple Formula for Calculating Bias-corrected AIC in Generalized Linear Models, SCANDINAVIAN JOURNAL OF STATISTICS, 41(2), 535-555, 201406
- Selecting a shrinkage parameter in structural equation modeling with a near singular covariance matrix by the GIC minimization method, HIROSHIMA MATHEMATICAL JOURNAL, 44(3), 315-326, 201411
- Asymptotic expansions of the distributions of MANOVA test statistics when the dimension is large, HIROSHIMA MATHEMATICAL JOURNAL, 44(3), 247-259, 201411
- Asymptotic expansions for a class of tests for a general covariance structure under a local alternative, JOURNAL OF MULTIVARIATE ANALYSIS, 102(6), 1080-1089, 201107
- Improvement of the quality of the chi-square approximation for the ADF test on a covariance matrix with a linear structure, JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 141(4), 1535-1542, 201104
- High-dimensional Edgeworth expansion of a test statistic on independence and its error bound, JOURNAL OF MULTIVARIATE ANALYSIS, 101(8), 1806-1813, 201009
- An improvement method of sliced inverse regression using principal component analysis, An improvement method of sliced inverse regression using principal component analysis, 4(2-3), 489-498, 2009
- ★, Optimal discriminant functions for normal populations, JOURNAL OF MULTIVARIATE ANALYSIS, 100(1), 58-69, 200901
- Asymptotic results in canonical discriminant analysis when the dimension is large compared to the sample size, JOURNAL OF STATISTICAL PLANNING AND INFERENCE, 138(11), 3457-3466, 20081101
- ★, Edgeworth expansion of Wilks' lambda statistic., J. Multivariate Anal., 97(9), 1958-1964, 20060801
- Contributions to multivariate analysis by Professor Yasunori Fujikoshi., J. Multivariate Anal., 97(9), 1914-1926, 20060801
- Asymptotic expansion for lack-of-fit test under nonnormality., Hiroshima Math. J., 36(1), 29-38, 20060301
- Berry-Esseen bound for high dimensional asymptotic approximation of Wilks' Lambda distribution, STATISTICS & PROBABILITY LETTERS, 76(12), 1191-1200, 20060701
- Bias corrections of some criteria for selecting multivariate linear models in a general nonnormal case., Amer. J. Math. Management Sci., 25(1), 221-268, 20050501
- Asymptotic results of a high dimensional Manova test and power comparison when the dimension is large compared to the sample size., J. Japan Statist. Soc., 34(1), 19-26, 20040301
- Asymptotic expansion of the null distribution of the likelihood ratio statistic for testing the equality of variances in a nonnormal one-way ANOVA model, Hiroshima Mathematical Journal, 33(1), 113-126, 20030301
- ★, Asymptotic expansions of the null distributions of test statistics for multivariate linear hypothesis under nonnormality, Hiroshima Mathematical Journal, 32(1), 17-50, 20020401
- Statistical discriminant analysis, Sugaku Expositions, 12(2), 185-199, 19990401
- Asymptotic expansions for the Studentized best linear discriminant function under two elliptical populations, American Journal of Mathematical and Management Sciences, MSI-2000, Vol. IV(no.1-2), 89-106, 19980401
- Asymptotic expansion of the joint distribution of sample mean vector and sample covariance matrix from an elliptical population, Hiroshima Mathematical Journal, 27(2), 295-305, 19970401
- Asymptotic expansions for the best linear discriminant functions, Hiroshima Mathematical Journal, 26(3), 593-603, 19960401
- ★, Discriminant analysis under elliptical populations, Hiroshima Mathematical Journal, 24(2), 257-298, 19940401
- ★, A class of tests for a general covariance structure, J. Multivariate Anal., 32(2), 313-325, 19900401
- ★, Comparison of linear and quadratic discriminant functions, Biometrika, 77(1), 227-229, 19900401
- Comparison of powers of a class of tests for covariance matrices, Hiroshima Mathematical Journal, 18(3), 599-611, 19880401
- Asymptotic expansion for the distribution of the discriminant function in the first order autoregressive processes, Hiroshima Mathematical Journal, 16(3), 625-629, 19860401
- Error bounds for high-dimensional Edgeworth expansions for some tests on covariance matrices, Proceedings of International Conference on Multivariate Statistical Modeling and High Dimensional Data Mining, Kayeseri, Turkey., 2010
- Selection of the linear and quadratic discriminant functions when the difference between two covariance matrices is small, J. Japan Statist. Soc., 47(2), 145-165, 2017

### Invited Lecture, Oral Presentation, Poster Presentation

- Large sample -High dimensional asymptotic expansions and its error bounds, Wakaki, Hirofumi, 16th JSS Spring Meeting, 2022/03/05, With Invitation, Japanese, The Japan Statistical Society, Keio University, Tokyo, Laplace's approximation formulae for the multivariate beta random matrix and the multivariate F random matrix are derived, and applied for the null distributions for MANOVA test statistics including Wilks's lambda, Lawley-Hottelling test, and Bartlett-Nanda-Pillai test. Error bounds for the approximation formulas for these three tests are also derived.

### Awards

- 2006/08, Jacob Wolfowitz Prize, Dr. Edward J. Dudewicz, Editor-in-Chief of AJMMS, Bias corrections of some criteria for selecting multivariate linear models in a general nonnormal case.

## External Funds

### Acceptance Results of Competitive Funds

- 2017, 2020
- KAKENHI, 2012, 2014
- KAKENHI, Development of two-stage methods for non-normal populations, 2009, 2011
- KAKENHI, Theory and Applications for Mathematical Methods in Statistical Science, 2007, 2010
- KAKENHI, 2006, 2008
- KAKENHI, The theory of growth data analysis and the development of its softwares, 1998, 2000
- KAKENHI, 1998, 1999
- KAKENHI, 1995, 1995

## Social Activities

### Organizing Academic Conferences, etc.

- 2001/01
- 1999/12
- 2005/01
- 2003/12
- 2006/08
- 2006/10
- Hiroshima Conference on Statistical Science 2016,, organaizer, 2016/12, 2016/12

### History as Peer Reviews of Academic Papers

- 2021, The Japan Statical Society Japanese Journal, Others, Referee, 1
- 2021, Hiroshima Mathematical Journal, Editor, Editor, 1