Skip to main content
SpringerLink
Log in

Matrix-trace Cauchy-Schwarz inequalities and applications in canonical correlation analysis

  • Articles
  • Published:
Statistical Papers Aims and scope Submit manuscript

Abstract

Various matrix-trace Cauchy-Schwarz and related inequalities involving positive semidefinite matrices are obtained. Applications of some of these results to canonical correlation analysis are presented.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  • Anderson, T.W. [1984] An Introduction to Multivariate Statistical Analysis, 2nd edn.Wiley, New York.

    MATH  Google Scholar 

  • Chaganty, N.R. [1993] Comment on “A matrix formulation on how deviant an observation can be”, by I. Olkin.The Amer. Statist., 47, 158.

    Google Scholar 

  • Giri, N. [1977] Multivariate Statistical Inference.Academic Press, New York.

    MATH  Google Scholar 

  • Kshirsagar, A.M. [1972] Multivariate Analysis.Dekker, New York.

    MATH  Google Scholar 

  • Leon, S.J. [1994] Maximizing bilinear forms subject to linear constraints.Linear Algebra Appl., 210, 49–58.

    Article  MathSciNet  MATH  Google Scholar 

  • Lin, C.T. [1990] Extremes of determinants and optimality of canonical variables.Commun. Statist. Simul. Comp., 19, 1415–1430.

    Article  MathSciNet  MATH  Google Scholar 

  • Magnus, J.R. and Neudecker, H. [1991] Matrix Differential Calculus with Applications in Statistics and Econometrics.Wiley, Chichester.

    MATH  Google Scholar 

  • Mardia, K.V., Kent, J.T. and Bibby, J.M. [1979] Multivariate Analysis.Academic Press, New York.

    MATH  Google Scholar 

  • Muirhead, R.J. [1982] Aspects of Multivariate Statistical Theory.Wiley, New York.

    Book  MATH  Google Scholar 

  • Neudecker, H. and Liu, S. [1994] Comment on “A matrix formulation on how deviant an observation can be”, by I. Olkin.The Amer. Statist., forthcoming.

  • Olkin, I. [1992] A matrix formulation on how deviant an observation can be.The Amer. Statist., 46, 205–209.

    MathSciNet  Google Scholar 

  • Press, S.J. [1972] Applied Multivariate Analysis.Holt, Rinehart and Winston, Inc., New York.

    MATH  Google Scholar 

  • Rao, C.R. [1973] Linear Statistical Inference and Its Applications, 2nd edn.Wiley, New York.

    Book  MATH  Google Scholar 

  • Rao, C.R. [1981] A lemma on g-inverse of a matrix and computation of correlation coefficients in the singular case.Commun. Statist. Theor. Meth., 10, 1–10.

    Article  MathSciNet  MATH  Google Scholar 

  • Toutenburg, H. [1992] Lineare Modelle.Physica-Verlag, Heidelberg.

    Book  Google Scholar 

  • Trenkler, G. [1994] Comment on “A matrix formulation on how deviant an observation can be”, by I.Olkin.The Amer. Statist., 48, 60–61.

    Article  Google Scholar 

  • Yanai, H. and Takane, Y. [1992] Canonical correlation analysis with linear constraints.Linear Algebra Appl., 176, 75–89.

    Article  MathSciNet  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Institute of Actuarial Science and Econometrics, University of Amsterdam, Roetersstraat 11, 1018 WB, Amsterdam, The Netherlands

    Shuangzhe Liu & Heinz Neudecker

Authors
  1. Shuangzhe Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Heinz Neudecker
    View author publications

    You can also search for this author in PubMed Google Scholar

Rights and permissions

Reprints and permissions

About this article

Cite this article

Liu, S., Neudecker, H. Matrix-trace Cauchy-Schwarz inequalities and applications in canonical correlation analysis. Stat Papers 36, 287–298 (1995). https://doi.org/10.1007/BF02926043

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02926043

Key words

Search

Navigation