zbMATH — the first resource for mathematics

Corrections to test statistics in principal Hessian directions. (English) Zbl 1157.62412

62H11 Directional data; spatial statistics
62H25 Factor analysis and principal components; correspondence analysis
Full Text: DOI
[1] Box, G.E.P., Some theorems on quadratic forms applied in the study of analysis of variance problems: I. effect of inequality of variance in one-way classification, Ann. math. statist., 25, 290-302, (1954) · Zbl 0055.37305
[2] Cook, R.D., Principal Hessian directions revisted, J. amer. statist. assoc., 93, 84-94, (1998)
[3] Cook, R.D., Rejoinder, J. amer. statist. assoc., 93, 98-100, (1998)
[4] Chou, C.-P.; Bentler, P.M.; Satorra, A., Scaled test statistics and robust standard errors for non-normal data in covariance structure analysis: A Monte Carlo study, British J. math. statist. psychol., 44, 347-357, (1991)
[5] Curran, P.S.; West, S.G.; Finch, J.F., The robustness of test statistics to nonnormality and specification error in confirmatory factor analysis, Psychol. methods, 1, 16-29, (1996)
[6] Fouladi, R.T., Type I error control of some covariance structure analysis techniques under conditions of multivariate nonnormality, Comput. sci. statist., 29, 526-532, (1997)
[7] Hu, L., Bentler, P.M., Kano, Y., 1992. Can test statistics in covariance structure analysis be trusted? Psychol. Bull. 112 351-362.
[8] Li, K.C., On principal hessian directions for data visualization and dimension reduction: another application of Stein’s lemma, J. amer. statist. assoc., 87, 1025-1039, (1992) · Zbl 0765.62003
[9] Li, K.C., Comment, J. amer. statist. assoc., 93, 94-97, (1998)
[10] Magnus, J.R., Neudecker, H., 1988. Matrix Differential Calculus with Applications in Statistics and Econometrics. Wiley, New York. · Zbl 0651.15001
[11] Rao, J.N.K.; Scott, A.J., On chi-squared tests for multi-way contingency tables with cell proportions estimated from survey data, Ann. statist., 12, 46-60, (1984) · Zbl 0622.62059
[12] Satterthwaite, F.E., Synthesis of variance, Psychometrika, 6, 309-316, (1941) · Zbl 0063.06742
[13] Satorra, A., Bentler, P.M., 1988. Scaling corrections for chi-square statistics in covariance structure analysis. 1988 Proceedings of the Business and Economic Statistics Section of the American Statistical Association, pp. 308-313.
[14] Satorra, A.; Bentler, P.M., Corrections to test statistics and standard errors in covariance structure analysis., (), 399-419
[15] Tierney, L., 1988. XLISP-STAT: a statistical environment based on the XLISP language (Version 2.0). Technical Report Number 528. School of Statistics, Minneapolis, MN.
[16] Wood, A.T.A., An F approximation to the distribution of a linear combination of chi-squared variables, Comm. statist. part B - simulation comput., 18, 1439-1456, (1989) · Zbl 0695.62028
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.