References
- Anderson, T. W., & Olkin, I. (1985). Maximum likelihood estimation of the parameters of a multivariate normal distribution. Linear Algebra and Its Applications, 70, 147–171. doi:10.1016/0024-3795(85)90049-7
- Chang, W.-Y., & Richards, D. S. P. (2009). Finite-sample inference with monotone incomplete multivariate normal data, I. Journal of Multivariate Analysis, 100(9), 1883–1899. doi:10.1016/j.jmva.2009.05.003
- Chang, W.-Y., & Richards, D. S. P. (2010). Finite-sample inference with monotone incomplete multivariate normal data, II. Journal of Multivariate Analysis, 101(3), 603–620. doi:10.1016/j.jmva.2009.09.011
- Cohen, N., Davidov, O., & Haitovsky, Y. (2008). Double sampling designs in multivariate linear models with missing variables. Communication in Statistics - Simulation and Computation, 37(6), 1156–1166. doi:10.1080/03610910801885993
- Fujikoshi, Y. (1980). Asymptotic expansions for the distributions of the sample roots under nonnormality. Biometrika, 67(1), 45–51. doi:10.2307/2335314
- Gupta, A. K., & Nagar, D. K. (1999). Matrix variate distributions. London: Chapman and Hall, CRC Press.
- Hao, J., & Krishnamoorthy, K. (2001). Inferences on a normal covariance matrix and generalized variance with monotone missing data. Journal of Multivariate Analysis, 78(1), 62–82. doi:10.1006/jmva.2000.1939
- Hyodo, M., Shutoh, N., Seo, T., & Pavlenko, T. (2016). Estimation of the covariance matrix with two-step monotone missing data. Communications in Statistics–Theory and Methods, 45(7), 1910–1922. doi:10.1080/03610926.2013.868085
- Kanda, T., & Fujikoshi, Y. (1998). Some basic properties of the MLE’s for a multivariate normal distribution with monotone missing data. American Journal of Mathematical and Management Sciences, 18(1–2), 161–190. doi:10.1080/01966324.1998.10737458
- Little, R. J. A. (1976). Inference about means from incomplete multivariate data. Biometrika, 63(3), 593–604. doi:10.2307/2335740
- Little, R. J. A., & Rubin, D. B. (2002). Statistical analysis with missing data, 2nd ed. New York, NY: Wiley-Interscience.
- Lu, G., & Copas, J. B. (2004). Missing at random, likelihood ignorability and model completeness. The Annals of Statistics, 32, 754–765. doi:10.1214/009053604000000166
- Richards, D. S. P., & Yamada, T. (2010). The Stein phenomenon for monotone incomplete multivariate normal data. Journal of Multivariate Analysis, 101(3), 657–678. doi:10.1016/j.jmva.2009.11.002
- Shutoh, N., Hyodo, M., & Seo, T. (2011). An asymptotic approximation for EPMC in linear discriminant analysis based on two-step monotone missing samples. Journal of Multivariate Analysis, 102(2), 252–263. doi:10.1016/j.jmva.2010.09.002
- Siotani, M., Hayakawa, T., & Fujikoshi, Y. (1985). Modern multivariate analysis, a graduate course and handbook. Ohio: American Sciences Press.
- Srivastava, M. S. (1985). Multivariate data with missing observations. Communications in Statistics - Theory and Methods, 14(4), 775–792. doi:10.1080/03610928508828949
- Sugiura, N. (1973). Derivatives of the characteristic root of a symmetric or a Hermitian matrix with two applications in multivariate analysis. Communications in Statistics, 1(5), 393–417. doi:10.1080/03610927308827036
- Sugiura, N. (1976). Asymptotic expansions of the distributions of the latent roots and the latent vector of the Wishart and multivariate F matrices. Journal of Multivariate Analysis, 6(4), 500–525. doi:10.1016/0047-259X(76)90002-6
- Tsukada, S. (2014). Unbiased estimator for a covariance matrix under two-step monotone incomplete sample. Communications in Statistics–Theory and Methods, 43(8), 1613–1629. doi:10.1080/03610926.2012.671881
- Tsukada, S. (2016). Asymptotic properties of a correlation matrix under a two-step monotone incomplete sample. Linear Algebra and Its Applications, 488, 86–101. doi:10.1016/j.laa.2015.09.035
- Yagi, A., & Seo, T. (2015). Tests for equality of mean vectors and simultaneous confidence intervals with two-step or three-step monotone missing data patterns. American Journal of Mathematical and Management Sciences, 34(3), 213–233. doi:10.1080/01966324.2015.1020403
- Yamada, T. (2013). Asymptotic properties of canonical correlation analysis for one group with additional observations. Journal of Multivariate Analysis, 114, 389–401. doi:10.1016/j.jmva.2012.08.001
- Yamada, T., Romer, M. M., & Richards, D. S. P. (2015). Kurtosis tests for multivariate normality with monotone incomplete data. Test, 24(3), 532–557. doi:10.1007/s11749-014-0423-1