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2016 | 4 | 1 | 283-295
Tytuł artykułu

Professor Haruo Yanai and multivariate analysis

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The late Professor Yanai has contributed to many fields ranging from aptitude diagnostics, epidemiology, and nursing to psychometrics and statistics. This paper reviews some of his accomplishments in multivariate analysis through his collaborative work with the present author, along with some untold episodes for the inception of key ideas underlying the work. The various topics covered include constrained principal component analysis, extensions of Khatri’s lemma, theWedderburn-Guttman theorem, ridge operators, generalized constrained canonical correlation analysis, and causal inference. A common thread running through all of them is projectors and singular value decomposition, which are the main subject matters of a recent monograph by Yanai, Takeuchi, and Takane [60].
Wydawca
Czasopismo
Rocznik
Tom
4
Numer
1
Strony
283-295
Opis fizyczny
Daty
otrzymano
2015-06-19
zaakceptowano
2016-06-10
online
2016-07-05
Twórcy
  • Department of Psychology, University of Victoria, Victoria, BC, Canada
Bibliografia
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  • [10] L. Hubert, J. Meulman, W. J. Heiser, Two purposes of matrix factorization: A historical appraisal, SIAM Review, 42 (2000), 68–82. [Crossref]
  • [11] H. Hwang, Y. Takane, Generalized Structured Component Analysis: A Component-Based Approach to Structural Equation Modeling (Chapman and Hall/CRC Press, Boca Raton, FL., 2014).
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  • [16] R. J. Light, B. H. Margolin, An analysis of variance of categorical data, J. Am. Stat. Assoc., 66 (1971), 534–544. [Crossref]
  • [17] S. Loisel, Y. Takane, Partitions of Pearson’s chi-square statistic for frequency tables: A comprehensive account, Computation. Stat., in press.
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  • [21] S. Puntanen, G. P. H. Styan, J. Isotalo, Matrix Tricks for Linear Statistical Models (Springer, Berlin, 2011).
  • [22] J. O. Ramsay, B. M. Silverman, Functional Data Analysis, Second Edition (Springer, New York, 2005).
  • [23] C. R. Rao, Linear Statistical Inference and Its Applications, Second Edition (Wiley, New York, 1973).
  • [24] C. R. Rao, S. K. Mitra, Generalized Inverse of Matrices amd Its Applications (Wiley, New York, 1971).
  • [25] C. R. Rao, H. Yanai, General definition and decomposition of projectors and some applications to statistical problems, J. Stat. Plan. Infer., 3 (1979), 1–17. [Crossref]
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  • [29] Y. Takane, Relationships among various kinds of eigenvalue and singular value decompositions, In: H. Yanai, A. Okada, K. Shigemasu, Y. Kano, and J. Meulman (Eds.), New Developments in Psychometrics (Springer, Tokyo, 2003), 45–56.
  • [30] Y. Takane, More on regularization and (generalized) ridge operators, In: K. Shigemasu, A. Okada, T. Imaizumi, T. Hoshino (Eds.), New Trends in Psychometrics (University Academic Press, Tokyo, 2008) 443–452.
  • [31] Y. Takane, Constrained Principal Component Analysis and Related Techniques (Chapman and Hall/CRC Press, Boca Raton, FL, 2013).
  • [32] Y. Takane, M. A. Hunter, Constrained principal component analysis: A comprehensive theory, Appl. Algebr. Eng. Comm., 12 (2001), 391–419. [Crossref]
  • [33] Y. Takane, M. A. Hunter, New family of constrained principal component analysis (CPCA), Linear Algebra Appl., 434 (2011), 2539–2555.
  • [34] Y. Takane, H. Hwang, Generalized constrained canonical correlation analysis, Multivar. Behav. Res., 37 (2002), 163–195. [Crossref]
  • [35] Y. Takane, H. Hwang, Regularized multiple correspondence analysis. In: J. Blasius, M. J. Greenacre (Eds.), Multiple correspondence analysis and related methods (Chapman and Hall, London, 2006) 259–279.
  • [36] Y. Takane, S. Jung, Regularized partial and/or constrained redundancy analysis, Psychometrika, 73 (2008), 671–690. [Crossref]
  • [37] Y. Takane, S. Jung, Regularized nonsymmetric correspondence analysis, Comput. Stat. Data An., 53 (2009), 3159–3170. [Crossref]
  • [38] Y. Takane, S. Jung, Tests of ignoring and eliminating in nonsymmetric correspondence analysis, Adv. Data Anal. Classif., 3 (2009), 315–340. [Crossref]
  • [39] Y. Takane, T. Shibayama, Principal component analysis with external information on both subjects and variables, Psyhometrika, 56 (1991), 97–120. [Crossref]
  • [40] Y. Takane, H. Yanai, On oblique projectors, Linear Algebra Appl., 289 (1999), 297–310.
  • [41] Y. Takane, H. Yanai, On the Wedderburn-Guttman theorem, Linear Algebra Appl. 410 (2005), 267–278.
  • [42] Y. Takane, H. Yanai, On ridge operators, Linear Algebra Appl., 428 (2008), 1778–1790.
  • [43] Y. Takane, L. Zhou, On two expressions of the MLE for a special case of the extended growth curve models, Linear Algebra Appl., 436 (2012), 2567–2577.
  • [44] Y. Takane, L. Zhou, Anatomy of Pearson’s chi-square statistic in three-way contingency tables, In: R. E. Millsap, L. A. van der Ark, D. M. Bolt, C. M. Woods (Eds.), New Developments in Quantitative Psychology (Springer, New York, 2013), 41–57.
  • [45] Y. Takane, H. Hwang, H. Abdi, Regularized multiple-set canonical correlation analysis, Psychometrika, 73 (2008), 753–775. [Crossref]
  • [46] Y. Takane, K. Jung, H. Hwang, Regularized growth curve models, Comput. Stat. Data An., 55 (2011), 1041–1052. [Crossref]
  • [47] Y. Takane, H. A. L. Kiers, J. de Leeuw, Component analysiswith different constraints on different dimensions, Psychometrika, 60 (1995), 259–280. [Crossref]
  • [48] Y. Takane, H. Yanai, H. Hwang, An improved method for generalized constrained canonical correlation analysis, Comp. Stat. Data An., 50 (2006), 221–241.
  • [49] Y. Takane, H. Yanai, S. Mayekawa, Relationships among several methods of linearly constrained correspondence analysis, Psychometrika, 56 (1991), 667–684. [Crossref]
  • [50] K. Takeuchi, H. Yanai, B. N.Mukherjee, The Foundation ofMultivariate Analysis (Wiley Eastern, New Delhi, and Halsted Press, New York, 1982).
  • [51] C. J. F. ter Braak, Canonical correspondence analysis: A new eigenvector technique for multivariate direct gradient analysis, Ecology, 67 (1986), 1167–1179.
  • [52] Y. Tian, The Moore-Penrose inverses of m× n blockmatrices and their applications, Linear Algebra Appl., 283 (1998), 35–60.
  • [53] Y. Tian, Upper and lower bounds for ranks ofmatrix expressions using generalized inverses, Linear Algebra Appl., 355 (2002), 187–214.
  • [54] Y. Tian, G. P. H. Styan,Onsomematrix equalities for generalized inverseswith applications, Linear Algebra Appl., 430 (2009), 2716–2733.
  • [55] A. P. Verbyla, A conditional derivation of residual maximum likelihood, Aust. J. Stat., 32 (1990), 227–230. [Crossref]
  • [56] J. H. M. Wedderburn, Lectures on Matrices, Colloquium Publication, Vol. 17 (American Mathematical Society, Providence, 1934).
  • [57] H. Yanai, Factor analysis with external criteria, Jpn. Psychol. Res., 12 (1970), 143–153.
  • [58] H. Yanai, Some generalized forms of least squares g-inverse, minimumnorm g-inverse and Moore-Penrose inversematrices, Comput. Stat. Data An., 10 (1990), 251–260. [Crossref]
  • [59] H. Yanai, Y. Takane, Canonical correlation analysis with linear constraints, Linear Algebra Appl., 176 (1992), 75–82.
  • [60] H. Yanai, K. Takeuchi, Y. Takane, Projection Matrices, Generalized Inverse Matrices, and Singular Value Decomposition (Springer, New York, 2011).
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.doi-10_1515_spma-2016-0027
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