Multivariate Distributions, Inference, Regression and Canonical Correlation

  • J. D. Jobson
Part of the Springer Texts in Statistics book series (STS)

Abstract

Before we introduce additional techniques for multivariate analysis, it is necessary to explain notation for multivariate random variables and samples. Since many multivariate inference procedures require a multivariate normal distribution assumption, an introduction to this distribution is also provided here. In addition, the chapter includes an outline of inference procedures for the mean vector and covariance matrix. In some applications multivariate random variables are partitioned into two or more subsets. The relationship between the variables in different sets is often of interest. In the last section of this chapter we outline the techniques of multivariate regression and canonical correlation in order to study the relationships between subsets of random variables.

Keywords

Covariance Resid Eosine Dition 

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Cited Literature and References

  1. 1.
    Anderson, T.W. (1984).An Introduction to Multivariate Statistical AnalysisSecond Edition. New York: John Wiley and Sons.MATHGoogle Scholar
  2. 2.
    Devlin, S.J., Gnanadesikan, R. and Kettering, J.R. (1975), “Robust Estimation and Outlier Detection with Correlation Coefficients,”Biometrika62, 531–545.MATHCrossRefGoogle Scholar
  3. 3.
    Geisser, S. and Greenhouse, S.W. (1958). “An Extension of Box’s Results on the Use of the F-Distribution in Multivariate Analysis,”Annals of Mathematical Statistics29, 885–891.MathSciNetMATHCrossRefGoogle Scholar
  4. 4.
    Gnanadesikan, R. (1977).Methods for Statistical Data Analysis of Multivariate Observations.New York: John Wiley and Sons.MATHGoogle Scholar
  5. 5.
    Hawkins, D.M. (1980).Identification of Outliers.London: Chapman and Hall.MATHGoogle Scholar
  6. 6.
    Huynh, H. and Feldt, L.S. (1970), “Conditions under which Mean Square Ratios in Repeated Measurement Designs have Exact F-Distributions,”Journal of the American Statistical Association65, 1582–1589.MATHCrossRefGoogle Scholar
  7. 7.
    Jobson, J.D. and Korkie, R. (1982). “Potential Performance and Tests of Portfolio Efficiency,”Journal of Financial Economics10, 433–456.CrossRefGoogle Scholar
  8. 8.
    Jobson, J.D. and Korkie, R. (1989). “A Performance Interpretation of Multivariate Tests of Asset Set Intersection, Spanning and Mean-Variance Efficiency,”Journal of Financial and Quantitative Analysis24, 185–204.CrossRefGoogle Scholar
  9. 9.
    Johnson, Richard A. and Wichern, Dean W. (1988).Applied Multivariate Statistical AnalysisSecond Edition. Englewood Cliffs, NJ: Prentice-Hall.MATHGoogle Scholar
  10. 10.
    Kryzanowski, W.J. (1988).Principles of Multivariate Analysis: A User’s Perspective.Oxford: Oxford University Press.Google Scholar
  11. 11.
    Mardia, K.V. (1970). “Measures of Multivariate Skewness and Kurtosis with Applications,”Biometrika57, 519–530.MathSciNetMATHCrossRefGoogle Scholar
  12. 12.
    Mardia, K.V., Kent, J.T. and Bibby, J.M. (1979).Multivariate Analysis.London: Academic Press.MATHGoogle Scholar
  13. 13.
    Morrison, Donald F. (1976).Multivariate Statistical MethodsSecond Edition. New York: McGraw-Hill.MATHGoogle Scholar
  14. 14.
    Press, S. James (1972).Applied Multivariate Analysis.New York: Holt, Rinehart, Winston.Google Scholar
  15. 15.
    Seber, G.A.F. (1984).Multivariate Observations.New York: John Wiley and Sons.MATHCrossRefGoogle Scholar
  16. 16.
    Stevens, James (1986).Applied Multivariate Statistics for the Social Sciences.Hillsdale, NJ: Lawrence Erlbaum Associates.Google Scholar
  17. 17.
    Zellner, A. (1962). “An Efficient Method of Estimating Seemingly Unrelated Regressions and Tests of Aggregation Bias,”Journal of the American Statistical Association57, 348–368.MathSciNetMATHCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media New York 1992

Authors and Affiliations

  • J. D. Jobson
    • 1
  1. 1.Faculty of BusinessUniversity of AlbertaEdmontonCanada

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