Likelihood Ratio Criterion for Testing Sphericity from a Multivariate Normal Sample with 2-step Monotone Missing Data Pattern

- Journal title : Communications for Statistical Applications and Methods
- Volume 12, Issue 2, 2005, pp.473-481
- Publisher : The Korean Statistical Society
- DOI : 10.5351/CKSS.2005.12.2.473

Title & Authors

Likelihood Ratio Criterion for Testing Sphericity from a Multivariate Normal Sample with 2-step Monotone Missing Data Pattern

Choi, Byung-Jin;

Choi, Byung-Jin;

Abstract

The testing problem for sphericity structure of the covariance matrix in a multivariate normal distribution is introduced when there is a sample with 2-step monotone missing data pattern. The maximum likelihood method is described to estimate the parameters on the basis of the sample. Using these estimates, the likelihood ratio criterion for testing sphericity is derived.

Keywords

2-step monotone missing data pattern;maximum likelihood estimation;sphericity;likelihood ratio criterion;

Language

English

References

1.

Amey, A.K.A and Gupta, A.K.(1992). Testing sphericity under a mixture model, Australian Journal of Statistics, Vol. 34, 451-460

2.

Anderson, T.W.(1957). Maximum likelihood estimates for a multivariate normal distribution when some observations are missing, Journal of the American Statistical Association, Vol. 52, 200-203

3.

Anderson, T.W.(1984). An Introduction to Multivariate Statistical Analysis, Wiley, New York

4.

Anderson, T.W. and Olkin, I.(1985). Maximum-likelihood estimation of the parameters of a multivariate normal distribution, Linear Algebra and its Applications, Vol. 70, 147-171

5.

Bhargava, R.P.(1975). Some one-sample hypothesis testing problems when there is a monotone sample from a multivariate normal population, Annals of the Institute of Statistical Mathematics, Vol. 27, 327-339

6.

Eaton, M.L. and Kariya, T.(1983). Multivariate tests with incomplete data, Annals of Statistics, Vol. 11, 654-665

7.

Gupta, A.K.(1977). On the distribution of sphericity test criterion in the multivariate Gaussian distribution, Australian Journal of Statistics, Vol. 19, 202-205

8.

Jinadasa, K.G. and Tracy, D.S.(1992). Maximum likelihood estimation for multivariate normal distribution with monotone sample, Communications in Statistics-Theory and Methods, Vol. 21, 41-50

9.

John, S.(1972). The distribution of a statistic used for testing sphericity of normal distributions, Biometrika, Vol. 59, 169-174

10.

Little, R.J.A and Rubin, D.B.(1987). Statistical Analysis with Missing Data, Wiley, New York

11.

Lord, F.M.(1955). Estimation of parameters from incomplete data, Journal of the American Statistical Association, Vol. 50, 870-876

12.

Mardia, K.V. and Jupp, P.E.(1999). Directional Statistics, Wiley, New York

13.

Mauchly, J.W.(1940). Significance test for sphericity of a normal n-variate distribution, Annals of Mathematical Statistics, Vol. 11, 204-209

14.

Nagar, D.K., Jain, S.K. and Gupta, A.K.(1991). Distribution of LRC for testing sphericity structure of a covariance matrix in multivariate normal distribution, Metron, Vol. 49, 435-457