Isaac Scientific Publishing

Journal of Advanced Statistics

Exact F-tests for the Mean of A Class of Elliptically Contoured Distributions

Download PDF (440.1 KB) PP. 212 - 217 Pub. Date: December 1, 2016

DOI: 10.22606/jas.2016.14004

Author(s)

  • Jiajuan Liang*
    College of Business, University of New Haven, West Haven, Connecticut, U.S.A.

Abstract

A class of F-tests are developed based on an i.i.d. sample from a subfamily of elliptically contoured distributions. The theory of spherical matrix distributions is employed for constructing the tests. The results from a Monte Carlo study on the empirical performance of the tests show that the tests can control type I error rates very well and have fairly good power performance even for very high dimension with a small sample size. An analysis on a real dataset in financial models illustrates possible applications of the proposed tests.

Keywords

Elliptically contoured distribution, F-test, high dimension, principal component, spherically symmetric distribution

References

[1] S. Cambanis, S. Huang and G. Simons, “On the theory of elliptically contoured distributions,” Journal of Multivariate Analysis, vol. 11, pp. 368–385, 1981.

[2] A. P. Dawid, “Spherical matrix distributions and a multivariate model” Journal of the Royal Statistical Society (Series B), vol. 39, pp. 254–261, 1977.

[3] A. P. Dawid, “Extendibility of spherical matrix distributions,” Journal of Multivariate Analysis, vol. 8, pp. 559–566, 1978.

[4] K. T. Fang, S. Kotz and K. W. Ng, Symmetric Multivariate and Related Distributions, Chapman and Hall, London and New York, 1990.

[5] K. T. Fang and Y. Zhang, Generalized Multivariate Analysis, Springer-Verlag and Science Press, Berlin/Beijing, 1990.

[6] M. R. Gibbons, S. Ross and J. Shanken, “A test of efficiency of a given portfolio,” Econometrica, vol. 57, pp. 1121–1152, 1989.

[7] A. K. Gupta and T. Varga, Elliptically Contoured Models in Statistics, Kluwer Academic Publishers, 1993.

[8] A. K. Gupta, T. Varga and T. Bodnar, Elliptically Contoured Models in Statistics and Portfolio Theory (Second Edition), Springer, 2013.

[9] J. Läuter, “Exact t and F tests for analyzing studies with multiple endpoints,” Biometrics, vol. 52, pp. 964–970, 1996.

[10] C. A. MacKinlay, “On multivariate tests of the CAPM,” Journal of Financial Economics, vol. 18, pp. 341–372, 1987.