The Distribution of a Consistent Estimator of the Traces Ratio of Two Population Covariance Matrices

Article Sidebar

PDF
Published: Dec 2, 2013
Keywords:
Multivariate Normal Distribution Covariance Matrices Sample Sizes Converge in Distribution

Main Article Content

Saowapha Chaipitak
Faculty of Science and Technology, Rajamangala University of Technology Thanyaburi
Boonyarit Choopradit
Faculty of Sciences and Industrial Technology, Prince of Songkla University

Abstract

In this paper, testing the hypothesis of the equality of two covariance matrices from independent multivariate normal populations is of interested. To test the hypothesis, a test statistic is proposed based on an unbiased and consistent estimator of the ratio between two traces of two population covariance matrices. The asymptotic distribution of the consistent estimator is investigated using the delta method. Finally, it converges in distribution to normal as the number of variables and sample sizes go forward to infinity.

Article Details

How to Cite
1.
Chaipitak S, Choopradit B. The Distribution of a Consistent Estimator of the Traces Ratio of Two Population Covariance Matrices. Prog Appl Sci Tech. [Internet]. 2013 Dec. 2 [cited 2024 Nov. 15];3(2):45-50. Available from: https://ph02.tci-thaijo.org/index.php/past/article/view/243233
Issue
Vol. 3 No. 2 (2013): July - December 2013
Section
Mathematics and Applied Statistics

References

T.W. Anderson, An Introduction to Multivariate Statistical Analysis, 2nd ed., New York, John Wiley & Sons, 1984.

S. Chaipitak and S. Chongcharoen, A test for testing the equality of two covariance matrices for high-dimensional data, J. Appl. Sci. 13 (2013), 270-277.

S. Chaipitak, Tests for covariance matrices with high-dimensional data, Ph.D. dissertation, National Institute of Development Administration, 2012.

Y. Fujikoshi, V. Ulyanov and R. Shimizu, Multivariate Statistics : High-Dimensional and Large-Sample Approximations, New Jersey, John Wiley & Sons, 2010.

J. Gamage, J and T. Mathew, Inference on mean sub-vectors of two multivariate normal populations with unequal covariance matrices, Stat. Probabil. Lett., 78 (2008), 420-425.

J.G. Ibrahim, M. Chen and R.J. Gray, Baysian models for gene expression with DNA microarray data. J. Am. Stat. Assoc. 97 (2002): 88-99.

D.E. Johnson, Applied Multivariate Methods for Data Analysts, California, Duxbury, 1998.

E.L. Lehmann and J.P. Romano, Testing Statistical Hypotheses, 3rd ed., New York, Springer, 2005.

J.R. Schott, A test for the equality of covariance matrices when the dimension is large relative to the sample sizes, Comput. Stat. Data. An., 51 (2007), 6535-6542.

M.S. Srivastava, Methods of multivariate statistics, New York, John Wiley & Sons, 2002.

M.S. Srivastava, Multivatiate theory for analyzing high-dimensional data. J. Japan. Statist. Soc., 37 (2007), 53-86.

M.S. Srivastava and H. Yanagihara, Testing the equality of several covariance matrices with fewer observations than the dimension., J. Multivariate Anal., 101 (2010), 1319-1329.