Statistical Inference of Moment Structures

Handbook of Latent Variable and Related Models

Volumn , Issue , 2007, Pages 229-260

  Shapiro, Alexander ^a  

^a Georgia Institute of Technology   (United States)

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EID: 44649164638     PISSN: None     EISSN: None     Source Type: Book    
DOI: 10.1016/B978-044452044-9/50014-8     Document Type: Chapter

References (40)

1. Amemiya Y., Anderson T.W. Asymptotic chi-square tests for a large class of factor analysis models. Annals of Statistics 1990, 18:1453-1463.
2. Anderson T.W., Amemiya Y. The Asymptotic normal distribution of estimators in Factor Analysis under general conditions. Annals of Statistics 1988, 16:759-771.
3. Anderson T.W., Rubin H. Statistical inference in factor analysis. Proceedings of the Third Berkley Symposium on Mathematical Statistics and Probability 1956, vol. 5:111-150. University of California Press, Berkeley, CA. J. Neyman (Ed.).
4. Bartholomew D.J. Ordered tests in the analysis of variance. Biometrika 1961, 48:325-332.
5. Bekker P.A., ten Berge J.M.F. Generic global identification in factor analysis. Linear Algebra and its Applications 1997, 264:255-263.
6. Bonnans J.F., Shapiro A. Perturbation Analysis of Optimization Problems 2000, Springer-Verlag, New York.
7. Browne M.W. Generalized least squares estimators in the analysis of covariance structures. South African Statistical Journal 1974, 8:1-24.
8. Browne M.W. Covariance structures. Topics in Applied Multivariate Analysis 1982, Cambridge University Press. D.M. Hawkins (Ed.).
9. Browne M.W. Asymptotically distribution-free methods in the analysis of covariance structures. British Journal of Mathematical and Statistical Psychology 1984, 37:62-83.
10. Browne M.W. Robustness in statistical inference in factor analysis and related models. Biometrika 1987, 74:375-384.
11. Browne M.W., Shapiro A. Robustness of normal theory methods in the analysis of linear latent variate models. British Journal of Mathematical and Statistical Psychology 1988, 41:193-208.
12. Chernoff H. On the distribution of the likelihood ratio. Ann. Math. Statist. 1954, 25:573-578.
13. Danskin J.M. The Theory of Max-Min and its Applications to Weapon Allocation Problems. Econometrics and Operations Research 1967, vol. 5. Springer-Verlag, Berlin and New York.
14. Fisher F.M. The Identification Problem in Econometrics 1966, McGraw-Hill, New York.
15. Jennrich R.I. Rotational equivalence of factor loading matrices with specified values. Psychometrika 1987, 43:421-426.
16. Jöreskog K.G. Structural equation models in the social sciences: specification, estimation and testing. Applications of Statistics 1977, 265-287. North-Holland, Amsterdam. P.R. Krishnaiah (Ed.).
17. Jöreskog K.G. Analysis of covariance structures (with discussion). Scandinavian Journal of Statistics 1981, 8:65-92.
18. Kano Y. Conditions on consistency of estimators in covariance structure model. Journal of the Japan Statistical Society 1986, 16:75-80.
19. Kudô A. A multivariate analogue of the one-sided test. Biometrika 1963, 50:403-418.
20. Ledermann W. On the rank of reduced correlation matrices in multiple factor analysis. Psychometrika 1937, 2:85-93.
21. Muirhead R.J. Aspects of Multivariate Statistical Theory 1982, Wiley, New York.
22. Muirhead R.J., Waternaux C.M. Asymptotic distribution in cannonical correlation analysis and other multivariate procedures for nonnormal populations. Biometrika 1980, 67:31-43.
23. Nüesch P.E. On the problem of testing location in multivariate populations for restricted alternatives. Ann. Math. Stat. 1966, 37:113-119.
24. Rothenberg T.J. Identification in parametric models. Econometrica 1971, 39:577-591.
25. Seber G.A.F. Linear Regression Analysis 1977, Wiley, New York.
26. Shapiro A. Asymptotic distribution theory in the analysis of covariance structures (a unified approach). South African Statistical Journal 1983, 17:33-81.
27. Shapiro A. A note on consistency of estimators in the analysis of moment structures. British Journal of Mathematical and Statistical Psychology 1984, 37:84-88.
28. Shapiro A. Identifiability of factor analysis: some results and open problems. Linear Algebra and its Applications 1985, 70:1-7.
29. Shapiro A. Asymptotic equivalence of minimum discrepancy function estimators to GLS estimators. Sourth African Statistical Journal 1985, 19:73-81.
30. Shapiro A. Second-order sensitivity analysis and asymptotic theory of parametrized nonlinear programs. Mathematical Programming 1985, 33:280-299.
31. Shapiro A. Asymptotic distribution of test statistics in the analysis of moment structures under inequality constraints. Biometrika 1985, 72:133-144.
32. Shapiro A. Asymptotic theory of overparametrized structural models. Journal of the American Statiscal Association 1986, 81:142-149.
33. Shapiro A. Robustness properties of the MDF analysis of moment structures. South African Statistical Journal 1987, 21:39-62.
34. Shapiro A. Towards a unified theory of inequality constrained testing in multivariate analysis. International Statistical Review 1988, 56:49-62.
35. Shapiro A., Browne M.W. Analysis of covariance structures under elliptical distributions. Journal of the American Statistical Association 1987, 82:1092-1097.
36. Silvapulle M.J., Sen P.K. Constrained Statistical Inference: Order, Inequality, and Shape Constraints 2005, Wiley, New York.
37. Steiger J.H., Shapiro A., Browne M.W. On the multivariate asymptotic distribution of sequential chi-square statistics. Psychometrika 1985, 50:253-264.
38. Tyler E.D. Radial estimates and the test for sphericity. Biometrika 1982, 69:429-436.
39. Tyler E.D. Robustness and efficiency properties of scatter matrices. Biometrika 1983, 70:411-420.
40. Wald A. Note on the identification of economic relations. Statistical Inference in Dynamic Economic Models 1950, John Wiley, New York. T.C. Koopmans (Ed.).