References
- Bai, J., & Li, K. (2012). Statistical analysis of factor models of high dimension. The Annals of Statistics, 40, 436–465. https://doi.org/https://doi.org/10.1214/11-AOS966
- Bai, J. (2013a). Fixed-effects dynamic panel models, a factor analytical method. Econometrica, 81, 285–314. https://doi.org/https://doi.org/10.3982/ECTA9409
- Bai, J. (2013b). Likelihood approach to dynamic panel models with interactive effects (Working Paper).
- Bentler, P. M., & Yuan, K.-H. (1999). Structural equation modeling with small samples: Test statistics. Multivariate Behavioral Research, 34, 181–197. https://doi.org/https://doi.org/10.1207/S15327906Mb340203
- Boomsma, A. (1982). The robustness of LISREL against small sample sizes in factor analysis models. In K. G. J. H. Wolds (Ed.), Systems under indirect observation: Causality, structure, prediction (Vol. 1, pp. 149–173). North-Holland.
- Browne, M. W. (1974). Generalized least squares estimators in the analysis of covariances. South African Statistical Journal, 8, 1–24. https://hdl.handle.net/10520/AJA0038271X_175
- Chen, S. X., Zhang, L.-X., & Zhong, P.-S. (2010). Tests for high-dimensional covariance matrices. Journal of the American Statistical Association, 105, 810–819. https://doi.org/https://doi.org/10.1198/jasa.2010.tm09560
- Deng, L., Yang, M., & Marcoulides, K. M. (2018). Structural equation modeling with many variables: A systematic review of issues and developments. Frontiers in Psychology, 9, 580. https://doi.org/https://doi.org/10.3389/fpsyg.2018.00580
- Fisher, T. J., Sun, X., & Gallagher, C. M. (2010). A new test for sphericity of the covariance matrix for high dimensional data. Journal of Multivariate Analysis, 101, 2554–2570. https://doi.org/https://doi.org/10.1016/j.jmva.2010.07.004
- Fouladi, R. T. (2000). Performance of modified test statistics in covariance and correlation structure analysis under conditions of multivariate nonnormality. Structural Equation Modeling, 7, 356–410. https://doi.org/https://doi.org/10.1207/S15328007SEM0703_2
- Fujikoshi, Y. (1970). Asymptotic expansions of the distributions of test statistics in multivariate analysis. Journal of Science of the Hiroshima University, 34, 73–144. https://doi.org/https://doi.org/10.32917/hmj/1206138381
- Gupta, A., & Nagar, D. (1999). Matrix variate distributions (Vol. 104). CRC Press.
- Hansen, L. P., Heaton, J., & Yaron, A. (1996). Finite-sample properties of some alternative GMM estimators. Journal of Business and Economic Statistics, 14, 262–280. https://doi.org/https://doi.org/10.1080/07350015.1996.10524656
- Hayakawa, K. (2019). Corrected goodness of fit test in covariance structure analysis. Psychological Methods, 24, 371–389. https://doi.org/https://doi.org/10.1037/met0000180
- Herzog, W., Boomsma, A., & Reinecke, S. (2007). The model-size effect on traditional and modified tests of covariance structures. Structural Equation Modeling, 14, 361–390. https://doi.org/https://doi.org/10.1080/10705510701301602
- Hu, L., Bentler, P. M., & Kano, Y. (1992). Can test statistics in covariance structure analysis be trusted? Psychological Bulletin, 112, 351. https://doi.org/https://doi.org/10.1037/0033-2909.112.2.351
- Jeffreys, H. (1946). An invariant form for the prior probability in estimation problems. Proceedings of the Royal Society of London. Series A: Mathematical, Physical and Engineering Sciences, 186, 453–461. https://doi.org/https://doi.org/10.1098/rspa.1946.0056
- John, S. (1971). Some optimal multivariate tests. Biometrika, 58, 123–127. https://doi.org/https://doi.org/10.1093/biomet/58.1.123
- John, S. (1972). The distribution of a statistic used for testing sphericity of normal distributions. Biometrika, 59, 169–173. https://doi.org/https://doi.org/10.1093/biomet/59.1.169
- Ledoit, O., & Wolf, M. (2002). Some hypothesis test for the covariance matrix when the dimension is large compared to the sample size. Annals of Statistics, 30, 1081–1102. https://doi.org/https://doi.org/10.1214/aos/1031689018
- Ledoit, O., & Wolf, M. (2012). Nonlinear shrinkage estimation of large-dimensional covariance matrices. Annals of Statistics, 40, 1024–1060. https://doi.org/https://doi.org/10.1214/12-AOS989
- Ledoit, O., & Wolf, M. (2015). Spectrum estimation: A unified framework for covariance matrix estimation and PCA in large dimensions. Journal of Multivariate Analysis, 139, 360–384. https://doi.org/https://doi.org/10.1016/j.jmva.2015.04.006
- Ledoit, O., & Wolf, M. (2018). Optimal estimation of a large-dimensional covariance matrix under Stein’s loss. Bernoulli, 24, 3791–3832. https://doi.org/https://doi.org/10.3150/17-BEJ979
- Mardia, K. V. (1970). Measures of multivariate skewness and kurtosis with applications. Biometrika, 57, 519–530. https://doi.org/https://doi.org/10.1093/biomet/57.3.519
- Moakher, M., & Batchelor, P. G. (2006). Symmetric positive-definite matrices: From geometry to applications and visualization. In J. Weickert, H. Hagen (Eds.), Visualization and processing of tensor fields. Mathematics and Visualization. (pp. 285–298). Berlin, Heidelberg: Springer. https://doi.org/https://doi.org/10.1007/3-540-31272-2_17
- Moshagen, M. (2012). The model size effect in SEM: Inflated goodness-of-fit statistics are due to the size of the covariance matrix. Structural Equation Modeling, 19, 86–98. https://doi.org/https://doi.org/10.1080/10705511.2012.634724
- Nevitt, J., & Hancock, G. R. (2004). Evaluating small sample approaches for model test statistics in structural equation modeling. Multivariate Behavioral Research, 39, 439–478. https://doi.org/https://doi.org/10.1207/S15327906MBR3903_3
- Schott, J. R. (2005). Testing for complete independence in high dimensions. Biometrika, 92, 951–956. https://doi.org/https://doi.org/10.1093/biomet/92.4.951
- Srivastava, M. S., Kollo, T., & Von Rosen, D. (2011). Some tests for the covariance matrix with fewer observations than the dimension under non-normality. Journal of Multivariate Analysis, 102, 1090–1103. https://doi.org/https://doi.org/10.1016/j.jmva.2011.03.003
- Srivastava, M. S., Yanagihara, H., & Kubokawa, T. (2014). Tests for covariance matrices in high dimension with less sample size. Journal of Multivariate Analysis, 130, 289–309. https://doi.org/https://doi.org/10.1016/j.jmva.2014.06.003
- Srivastava, M. S. (2005). Some tests concerning the covariance matrix in high dimensional data. Journal of Japanese Statistical Society, 35, 251–272. https://doi.org/https://doi.org/10.14490/jjss.35.251
- Stein, C. (1975). Estimation of a covariance matrix. Rietz lecture, 39th annual meeting IMS.
- Stein, C. (1986). Lectures on the theory of estimation of many parameters. Journal of Mathematical Sciences, 34, 1373–1403. https://doi.org/https://doi.org/10.1007/BF01085007
- Swain, A. (1975). A class of factor analysis estimation procedures with common asymptotic sampling properties. Psychometrika, 40, 315–335. https://doi.org/https://doi.org/10.1007/BF02291761
- Tian, Y., & Yuan, K.-H. (2019). Mean and variance corrected test statistics for structural equation modeling with many variables. Structural Equation Modeling, 26, 827–846. https://doi.org/https://doi.org/10.1080/10705511.2019.1598865
- Tsukuma, H. (2005). Estimating the inverse matrix of scale parameters in an elliptically contoured distribution. Journal of the Japan Statistical Society, 35, 21–39. https://doi.org/https://doi.org/10.14490/jjss.35.21
- Watamori, Y. (1990). On the moments of traces of Wishart inverted Wishart matrices. South African Statistical Journal, 24, 153–176. https://hdl.handle.net/10520/AJA0038271X_355
- Yanagihara, H. (2007). A family of estimators for multivariate kurtosis in a nonnormal linear regression model. Journal of Multivariate Analysis, 98, 1–29. https://doi.org/https://doi.org/10.1016/j.jmva.2005.05.015
- Yuan, K.-H., Fan, C., & Zhao, Y. (2019). What causes the mean bias of the likelihood ratio statistic with many variables?. Multivariate Behavioral Research, 54, 840–855. https://doi.org/https://doi.org/10.1080/00273171.2019.1596060
- Yuan, K., & Bentler, P. (1997). Generating multivariate distributions with specified marginal skewness and kurtosis. In W. Bandilla & F. F (Eds.), SoftStat’97-Advances in statistical Software 6- (pp. 385–391). Lucius and Lucius.