Browse > Article
http://dx.doi.org/10.5351/CKSS.2005.12.2.473

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

Choi, Byung-Jin (Department of Applied Information Statistics, Kyonggi University)
Publication Information
Communications for Statistical Applications and Methods / v.12, no.2, 2005 , pp. 473-481 More about this Journal
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;
Citations & Related Records
연도 인용수 순위
  • Reference
1 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   DOI   ScienceOn
2 Lord, F.M.(1955). Estimation of parameters from incomplete data, Journal of the American Statistical Association, Vol. 50, 870-876   DOI   ScienceOn
3 Amey, A.K.A and Gupta, A.K.(1992). Testing sphericity under a mixture model, Australian Journal of Statistics, Vol. 34, 451-460   DOI   ScienceOn
4 Little, R.J.A and Rubin, D.B.(1987). Statistical Analysis with Missing Data, Wiley, New York
5 Mauchly, J.W.(1940). Significance test for sphericity of a normal n-variate distribution, Annals of Mathematical Statistics, Vol. 11, 204-209   DOI   ScienceOn
6 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   DOI
7 Eaton, M.L. and Kariya, T.(1983). Multivariate tests with incomplete data, Annals of Statistics, Vol. 11, 654-665   DOI   ScienceOn
8 Gupta, A.K.(1977). On the distribution of sphericity test criterion in the multivariate Gaussian distribution, Australian Journal of Statistics, Vol. 19, 202-205   DOI
9 John, S.(1972). The distribution of a statistic used for testing sphericity of normal distributions, Biometrika, Vol. 59, 169-174   DOI   ScienceOn
10 Mardia, K.V. and Jupp, P.E.(1999). Directional Statistics, Wiley, New York
11 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
12 Provost, S.B.(1990). Estimators for the parameters of a multivariate normal random vector with incomplete data on two sub vectors and test of independence, Computational Statistics and Data Analysis, Vol. 9, 37-46   DOI   ScienceOn
13 Sugira, N.(1972). Locally best invariant test for sphericity and the limiting distributions, Annals of Mathematical Statistics, Vol. 43, 1312-1316   DOI   ScienceOn
14 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   DOI   ScienceOn
15 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   DOI   ScienceOn
16 Anderson, T.W.(1984). An Introduction to Multivariate Statistical Analysis, Wiley, New York