Multivariate Analysis

 

               

 

“Everything is related with every other thing, and this relation involves the emergence of a relational quality. The qualities cannot be known a priori, though a good number of them can be deduced from certain fundamental characteristics”.

Jaina philosophy.

 

 The Jaina Philosophy of Non-Absolution by S. Mookerjee, q.v. Mahalanobis

(1957).

 

Multivariate Analysis deals with observations on more than one variable where there is some inherent interdependence between the variables. Its applications appear in every walk of life.

 

See also:

http://en.wikipedia.org/wiki/Multivariate_analysis

 

Multivariate Analysis of Mardia’s measure of skewness and kurtosis, multivariate permutation test, Mardia’s multivariate Pareto distribution.

Books:

1970    Families of Bivariate Distributions. Charles Griffin, London.

1979    Multivariate Analysis (with J. T. Kent and J. M. Bibby). Academic Press, New York, 1979. Translated in Persian.

            The data for this book have now been collected onto a web page:

            http://www.maths.leeds.ac.uk/~charles/mva-data/mva.html

 

Edited Volume:

2002    Statistics of Large Datasets, co-editors: R. G. Aykroyd and P. McDonnell. LASR Proceedings: Leeds University Press.

Papers in Journals:

1962    Multivariate Pareto distributions. Ann. Math. Statist. 33, 1008-1015.

1967    Some contributions to contingency-type bivariate distributions. Biometrika 54, 235-249.

1967    Correlation of the ranges of correlated samples. Biometrika 54, 529-539.

1968    Small sample power of a non-parametric test for the bivariate two-sample location problem. J. Roy. Statist. Soc. Ser. B 30, 83-92.

1969    On the null distribution of a non-parametric test for the two-sample problem. J. Roy. Statist. Soc. Ser. B 39, 98-102.

1969    The performance of some tests of independence for contingency-type bivariate distributions. Biometrika 56, 449-451.

1970    Measures of multivariate skewness and kurtosis with applications. Biometrika 57, 519-530.

1970    A bivariate non-parametric c-sample test. J. Roy. Statist. Soc. Ser. B 32, 74-87.

1970    Some problems of fitting for contingency-type bivariate distributions. J. Roy. Statist. Soc. Ser. B 32, 254-264.

1971    The effect of non-normality on some multivariate tests and robustness to non-normality in linear model. Biometrika 58, 105-121.

1973    Multivariate analysis and its applications: A report on Hull conference (with J. C. Gower). J. Roy. Statist. Soc. Ser. C 23, 60-66.

1974    Measures of multivariate skewness and kurtosis (with P. J. Zemroch). J. Roy. Statist. Soc. Ser. C 24, 262-265.           

1975    Assessment of multinormality and the robustness of Hotelling’s T2  test. J. Roy. Statist. Soc. Ser. C 24, 163-171.

1977    On some tests for the bivariate two-sample location problem (with B.D. Spurr). J. Amer. Statist. Assoc. 72, 994-995.

1978    Density preserving statistics and densities for sample means (with P.E. Jupp). Ann. Probab. 6, 688-694.

1991    Rao’s score test of goodness-of-fit and independence (with J. T. Kent). Biometrika 28, 355-63.

Paper in Edited Volume:

1977    Mahalanobis distances and angles. Multivariate Analysis IV (P. R. Krishnaiah ed.), 495-511. North Holland, Amsterdam.