# Multivariate Distributions, Inference, Regression and Canonical Correlation

• J. D. Jobson
Chapter
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 Matrix Maximum Likelihood Estimator Mahalanobis Distance Canonical Correlation Canonical Correlation Analysis
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

## Preview

Unable to display preview. Download preview PDF.

## Cited Literature and References

1. 1.
Anderson, T.W. (1984).An Introduction to Multivariate Statistical AnalysisSecond Edition. New York: John Wiley and Sons.
2. 2.
Devlin, S.J., Gnanadesikan, R. and Kettering, J.R. (1975), “Robust Estimation and Outlier Detection with Correlation Coefficients,”Biometrika62, 531–545.
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.
4. 4.
Gnanadesikan, R. (1977).Methods for Statistical Data Analysis of Multivariate Observations.New York: John Wiley and Sons.
5. 5.
Hawkins, D.M. (1980).Identification of Outliers.London: Chapman and Hall.
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.
7. 7.
Jobson, J.D. and Korkie, R. (1982). “Potential Performance and Tests of Portfolio Efficiency,”Journal of Financial Economics10, 433–456.
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.
9. 9.
Johnson, Richard A. and Wichern, Dean W. (1988).Applied Multivariate Statistical AnalysisSecond Edition. Englewood Cliffs, NJ: Prentice-Hall.
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.
12. 12.
Mardia, K.V., Kent, J.T. and Bibby, J.M. (1979).Multivariate Analysis.London: Academic Press.
13. 13.
Morrison, Donald F. (1976).Multivariate Statistical MethodsSecond Edition. New York: McGraw-Hill.
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.
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.