On asymptotic distributions of normal theory MLE in covariance structure analysis under some nonnormal distributions

Statistics and Probability Letters

Volumn 42, Issue 2, 1999, Pages 107-113

  Yuan, Ke Hai ^a   Bentler, Peter M ^b  

^a UNIVERSITY OF NORTH TEXAS   (United States)

^b UNIVERSITY OF CALIFORNIA   (United States)

Author keywords

Factor analysis; MLE; Pseudo elliptical distribution

Indexed keywords

EID: 0033115516     PISSN: 01677152     EISSN: None     Source Type: Journal    
DOI: 10.1016/S0167-7152(98)00171-0     Document Type: Article

References (12)

1. Anderson, T.W., Amemiya, Y., 1988. The asymptotic normal distribution of estimators in factor analysis under general conditions. Ann. Statist. 16, 759-771.
2. Browne, M.W., 1984. Asymptotic distribution-free methods for the analysis of covariance structures. British J. Math. Statist. Psychol. 37, 62-83.
3. Fang, K.-T., Kotz, S., Ng., K.W., 1990. Symmetric Multivariate and Related Distributions. Chapman & Hall, London.
4. Kano, Y., 1992. Robust statistics for test-of-independence and related structural models. Statist. Probab. Letters 15, 21-26.
5. Magnus, J.R., Neudecker, H., 1988. Matrix Differential Calculus with Applications in Statistics and Econometrics. Wiley, New York.
6. Mardia, K.V., 1970. Measure of multivariate skewness and kurtosis with applications. Biometrika 57, 519-530.
7. Satorra, A., Bentler, P.M., 1988. Scaling corrections for chi-square statistics in covariance structure analysis. American Statistical Association, 1988. Proc. Business and Economics Sections, American Statistical Association, VA, pp. 308-313.
8. Satorra, A., Bentler, P.M., 1994. Corrections to test statistics and standard errors in covariance structure analysis. In: von Eye, A., Clogg, C.C. (Lds.), Latent Variables Analysis: Applications for Developmental Research, Sage, Thousand Oaks, CA, pp. 399-419.
9. Shapiro, A., Browne, M., 1987. Analysis of covariance structures under elliptical distributions. J. Amer. Statist. Assoc. 82, 1092-1097.
10. Yuan, K.-H., Bentler, P.M., 1997a. Mean and covariance structure analysis: theoretical and practical improvements. J. Amer. Statist. Assoc. 92, 767-774.
11. Yuan, K.-H., Bentler, P.M., 1997b. Generating multivariate distributions with specified marginal skewness and kurtosis. In: Bandilla, W., Faulbaum, F. (Eds.), SoftStat'97: Advances in Statistical Software 6. Lucius & Lucius, Stuttgart, pp. 385-391.
12. Yuan, K.-H., Bentler, P.M., 1999. On normal theory and associated test statistics in covariance structure analysis under two classes of nonnormal distributions. Statist. Sinica, to appear.