Hirofumi Wakaki

Last Updated :2024/06/04

Affiliations, Positions
Graduate School of Advanced Science and Engineering, Professor
E-mail
wakakihiroshima-u.ac.jpwakakimath.sci.hiroshima-u.ac.jp
Other Contact Details
"1-3-1 KAGAMIYAMA, HIGASHI-HIROSHIMA, 739-8526 JAPAN", Japan
TEL : (+81)82-424-7359 FAX : (+81)82-424-7359

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

  1. 2024, Liberal Arts Education Program1, 4Term, Fundamental Data Science
  2. 2024, Undergraduate Education, Intensive, Basic mathematics
  3. 2024, Liberal Arts Education Program1, 1Term, Introductory Seminar for First-Year Students
  4. 2024, Undergraduate Education, First Semester, Special Study of Mathematics and Informatics for Graduation
  5. 2024, Undergraduate Education, Second Semester, Special Study of Mathematics and Informatics for Graduation
  6. 2024, Undergraduate Education, 4Term, Sparse covariance estimation
  7. 2024, Undergraduate Education, 2Term, Nonparametric analysis
  8. 2024, Graduate Education (Master's Program) , 2Term, Mathematical Omnibus
  9. 2024, Graduate Education (Master's Program) , Academic Year, Mathematical Statistics Seminar
  10. 2024, Graduate Education (Master's Program) , 1Term, Probability and Mathematical Statistics B
  11. 2024, Graduate Education (Master's Program) , 4Term, Topics in Probability and Mathematical Statistics B
  12. 2024, Graduate Education (Master's Program) , 4Term, Special Lectures in Mathematics
  13. 2024, Graduate Education (Master's Program) , Academic Year, Exercises in Mathematics
  14. 2024, Graduate Education (Master's Program) , First Semester, Exercises in Mathematics A
  15. 2024, Graduate Education (Master's Program) , Second Semester, Exercises in Mathematics B
  16. 2024, Graduate Education (Master's Program) , Academic Year, Seminar in Mathematics
  17. 2024, Graduate Education (Doctoral Program) , Academic Year, Seminar in Mathematics

Research Activities

Academic Papers

  1. Laplace expansion for Bartlett--Nanda--Pillai's test statistic and its error bound, Teor. Veroyatnost. i Primenen, 68(4), 705-718, 2023
  2. 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
  3. Principalcomponents regression by using generalized principal components analysis., J. Japan Statist. Soc., 43(1), 57-78, 2013
  4. 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
  5. 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
  6. EPMC estimation in discriminant analysis when the dimension and sample sizes are large, HIROSHIMA MATHEMATICAL JOURNAL, 47(1), 43-62, 201703
  7. 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
  8. 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
  9. ★, 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
  10. Simple Formula for Calculating Bias-corrected AIC in Generalized Linear Models, SCANDINAVIAN JOURNAL OF STATISTICS, 41(2), 535-555, 201406
  11. 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
  12. Asymptotic expansions of the distributions of MANOVA test statistics when the dimension is large, HIROSHIMA MATHEMATICAL JOURNAL, 44(3), 247-259, 201411
  13. 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
  14. 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
  15. High-dimensional Edgeworth expansion of a test statistic on independence and its error bound, JOURNAL OF MULTIVARIATE ANALYSIS, 101(8), 1806-1813, 201009
  16. 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
  17. ★, Optimal discriminant functions for normal populations, JOURNAL OF MULTIVARIATE ANALYSIS, 100(1), 58-69, 200901
  18. 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
  19. ★, Edgeworth expansion of Wilks' lambda statistic., J. Multivariate Anal., 97(9), 1958-1964, 20060801
  20. Contributions to multivariate analysis by Professor Yasunori Fujikoshi., J. Multivariate Anal., 97(9), 1914-1926, 20060801
  21. Asymptotic expansion for lack-of-fit test under nonnormality., Hiroshima Math. J., 36(1), 29-38, 20060301
  22. Berry-Esseen bound for high dimensional asymptotic approximation of Wilks' Lambda distribution, STATISTICS & PROBABILITY LETTERS, 76(12), 1191-1200, 20060701
  23. 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
  24. 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
  25. 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
  26. ★, Asymptotic expansions of the null distributions of test statistics for multivariate linear hypothesis under nonnormality, Hiroshima Mathematical Journal, 32(1), 17-50, 20020401
  27. Statistical discriminant analysis, Sugaku Expositions, 12(2), 185-199, 19990401
  28. 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
  29. 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
  30. Asymptotic expansions for the best linear discriminant functions, Hiroshima Mathematical Journal, 26(3), 593-603, 19960401
  31. ★, Discriminant analysis under elliptical populations, Hiroshima Mathematical Journal, 24(2), 257-298, 19940401
  32. ★, A class of tests for a general covariance structure, J. Multivariate Anal., 32(2), 313-325, 19900401
  33. ★, Comparison of linear and quadratic discriminant functions, Biometrika, 77(1), 227-229, 19900401
  34. Comparison of powers of a class of tests for covariance matrices, Hiroshima Mathematical Journal, 18(3), 599-611, 19880401
  35. Asymptotic expansion for the distribution of the discriminant function in the first order autoregressive processes, Hiroshima Mathematical Journal, 16(3), 625-629, 19860401
  36. 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
  37. 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

  1. 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

  1. 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

  1. 2017, 2020
  2. KAKENHI, 2012, 2014
  3. KAKENHI, Development of two-stage methods for non-normal populations, 2009, 2011
  4. KAKENHI, Theory and Applications for Mathematical Methods in Statistical Science, 2007, 2010
  5. KAKENHI, 2006, 2008
  6. KAKENHI, The theory of growth data analysis and the development of its softwares, 1998, 2000
  7. KAKENHI, 1998, 1999
  8. KAKENHI, 1995, 1995

Social Activities

Organizing Academic Conferences, etc.

  1. 2001/01
  2. 1999/12
  3. 2005/01
  4. 2003/12
  5. 2006/08
  6. 2006/10
  7. Hiroshima Conference on Statistical Science 2016,, organaizer, 2016/12, 2016/12

History as Peer Reviews of Academic Papers

  1. 2021, The Japan Statical Society Japanese Journal, Others, Referee, 1
  2. 2021, Hiroshima Mathematical Journal, Editor, Editor, 1