Arnold,, S. F. (1981). The theory of linear models and multivariate analysis. New York, NY: Wiley.
Barton,, T. A., & Fuhrmann,, D. R. (1993). Covariance structures for multidimensional data. Multidimensional Systems and Signal Processing, 4, 111–123.
Burg,, J. P., Luenberger,, D. G., & Wenger,, D. L. (1982). Estimation of structured covariance matrices. Proceedings of the IEEE, 70, 963–974.
Byakagaba, M. (1987). Apport de la matrice normale aux modèles d`analyse de la variance et des mesures répétées. (D.Sc. Dissertation). Université catholique de Louvain, Louvain‐la‐Neuve, Belgium.
Cressie,, N. A. C. (1993). Statistics for spatial data, Revised Edition. New York, NY: Wiley.
de Munck,, J. C., Huizenga,, H. M., Waldorp,, L. J., & Heethaar,, R. M. (2002). Estimating stationary dipoles from MEG/EEG data contaminated with spatially and temporally correlated background noise. IEEE Transactions on Signal Processing, 50, 1565–1572.
Diggle,, P. J., Liang,, K. Y., & Zeger,, S. L. (1996). Analysis of longitudinal data. Oxford, England: Oxford University Press.
Dutilleul, P. (1990). Apport en analyse spectrale d`un périodogramme modifié et modélisation des séries chronologiques avec répétitions en vue de leur comparaison en fréquence. (D.Sc. (Mathematics) Dissertation). Université catholique de Louvain, Louvain‐la‐Neuve, Belgium.
Dutilleul,, P. (1994). Maximum likelihood estimation for the matrix normal distribution. Report Series. Montréal, Canada: Department of Mathematics and Statistics, McGill University.
Dutilleul,, P. (1999). The MLE algorithm for the matrix normal distribution. Journal of Statistical Computation and Simulation, 64, 105–123.
Dutilleul,, P. (2011). Spatio‐temporal heterogeneity: Concepts and analyses (pp. 15–57). Cambridge, England: Cambridge University Press.
Dutilleul,, P., & Pinel‐Alloul,, B. (1996). A doubly multivariate model for statistical analysis of spatio‐temporal environmental data. Environmetrics, 7, 551–566.
Filipiak,, K., Klein,, D., & Roy,, A. (2016). Score test for a separable covariance structure with the first component as compound symmetric correlation matrix. Journal of Multivariate Analysis, 150, 105–124.
Filipiak,, K., Klein,, D., & Roy,, A. (2017). A comparison of likelihood ratio tests and Rao`s score test for three separable covariance matrix structures. Biometrical Journal, 59, 192–215.
Finn,, J. D. (1974). A general model for multivariate analysis. New York, NY: Holt, Rinehart and Winston.
Galecki,, A. T. (1994). General class of covariance structures for two or more repeated factors in longitudinal data analysis. Communications in Statistics – Theory and Methods, 23, 3105–3119.
Graybill,, F. A. (1983). Matrices with applications in statistics (2nd ed.). Belmont, TN: Wadsworth.
Hoff,, P. (2011). Separable covariance arrays via the Tucker product, with applications to multivariate relational data. Bayesian Analysis, 6, 1–18.
Kotz,, S., Balakrishnan,, N., Read,, C. B., & Vidakovic,, B. (Eds.). (2006). Encyclopedia of statistical sciences (Vol. 1, 2nd ed.). New York, NY: Wiley.
Krishnaiah,, P. R. (Ed.). (1980). Analysis of variance Handbook of statistics (Vol. 1). Amsterdam, the Netherlands: North‐Holland.
Lee,, C. H., Dutilleul,, P., & Roy,, A. (2010). Comment on “Models with a Kronecker product covariance structure: Estimation and testing” by Srivastava MS, von Rosen T, von Rosen D. Mathematical Methods of Statistics, 19, 88–90.
Lehmann,, E. L., & Romano,, J. P. (2005). Testing statistical hypotheses (3rd ed.). New York, NY: Springer.
Leiva,, R., & Roy,, A. (2009). Classification rules for triply multivariate data with an AR(1) correlation structure on the repeated measures over time. Journal of Statistical Planning and Inference, 139, 2598–2613.
Leiva,, R., & Roy,, A. (2014). Classification of higher‐order data with separable covariance and structured multiplicative or additive mean models. Communications in Statistics – Theory and Methods, 43, 989–1012.
Lu, N, Zimmerman, D. (2004). On likelihood‐based inference for a separable covariance matrix. Technical Report. Department of Statistics and Actuarial Science, University of Iowa, Iowa City, IA.
Lu,, N., & Zimmerman,, D. (2005). The likelihood ratio test for a separable covariance matrix. Statistics and Probability Letters, 73, 449–457.
Manceur,, A. M., Beaulieu,, J., Han,, L., & Dutilleul,, P. (2012). A multidimensional statistical model for wood data analysis, with density estimated from CT scanning data as an example. Canadian Journal of Forest Research, 42, 1038–1049.
Manceur,, A. M., & Dutilleul,, P. (2013a). Unbiased modified likelihood ratio tests for simple and double separability of a variance‐covariance structure. Statistics and Probability Letters, 83, 631–636.
Manceur,, A. M., & Dutilleul,, P. (2013b). Maximum likelihood estimation for the tensor normal distribution: Algorithm, minimum sample size, and empirical bias and dispersion. Journal of Computational and Applied Mathematics, 239, 37–49.
Mardia,, K. V. (1980). Tests of univariate and multivariate normality. In P. R. Krishnaiah, (Ed.), Analysis of variance (handbook of statistics, 1) (pp. 279–320). Amsterdam, the Netherlands: North‐Holland.
Mardia,, K. V., & Goodall,, C. (1993). Spatial‐temporal analysis of multivariate environmental monitoring data. In G. P. Patil, & C. R. Rao, (Eds.), Multivariate environmental statistics Series in Probability and Statistics (Vol. 6, pp. 347–385). New York, NY: North‐Holland.
McKiernan,, S. H., Colman,, R. J., Lopez,, M., Beasley,, T. M., Weindruch,, R., & Aiken,, J. M. (2009). Longitudinal analysis of early stage Sarcopenia in aging rhesus monkeys. Experimental Gerontology, 44, 170–176.
Mitchell,, M. W., Genton,, M. G., & Gumpertz,, M. L. (2005). Testing for separability of space‐time covariances. Environmetrics, 16, 819–831.
Mitchell,, M. W., Genton,, M. G., & Gumpertz,, M. L. (2006). A likelihood ratio test for separability of covariances. Journal of Multivariate Analysis, 97, 1025–1043.
Muirhead,, R. J. (1982). Aspects of multivariate statistical theory. New York, NY: Wiley.
Ohlson,, M., Ahmad,, M. R., & von Rosen,, D. (2013). The multilinear normal distribution: Introduction and some basic properties. Journal of Multivariate Analysis, 113, 37–47.
Patterson,, H. D., & Thompson,, R. (1971). Recovery of inter‐block information when block sizes are unequal. Biometrika, 58, 545–554.
Rao,, C. R. (1984). Linear statistical inference and its applications (2nd ed.). New Delhi, India: Wiley.
Rao,, C. R. (2005). Score test: Historical review and recent developments. In N. Balakrishnan,, N. Kannan,, & H. N. Nagaijuna, (Eds.), Advances in ranking and selection, multiple comparisons, and reliability (pp. 3–20). Boston, MA: Birkhäuser.
Roś,, B., Bijma,, F., de Munck,, J. C., & de Gunst,, M. C. M. (2016). Existence and uniqueness of the maximum likelihood estimator for models with a Kronecker product covariance structure. Journal of Multivariate Analysis, 143, 345–361.
Roy,, A., & Khattree,, R. (2005). On implementation of a test for Kronecker product covariance structure for multivariate repeated measures data. Statistical Methodology, 2, 297–306.
Roy,, A., & Leiva,, R. (2008). Likelihood ratio tests for triply multivariate data with structured correlation on spatial repeated measurements. Statistics and Probability Letters, 78, 1971–1980.
Simpson,, S. L. (2010). An adjusted likelihood ratio test for separability in unbalanced multivariate repeated measures data. Statistical Methodology, 7, 511–519.
Singull,, M., Ahmad,, M. R., & von Rosen,, D. (2012). More on the Kronecker structured covariance matrix. Communications in Statistics – Theory and Methods, 41, 2512–2523.
Soloveychik,, I., & Trushin,, D. (2016). Gaussian and robust Kronecker product covariance estimation: Existence and uniqueness. Journal of Multivariate Analysis, 149, 92–113.
Srivastava,, M., von Rosen,, T., & von Rosen,, D. (2008). Models with a Kronecker product covariance structure: Estimation and testing. Mathematical Methods of Statistics, 17, 357–370.
Stuart,, A., Ord,, K., & Arnold,, S. (1999). Kendall`s advanced theory of statistics, volume 2A, classical inference and the linear model (6th ed.). London, England: Arnold.
Werner,, K., Jansson,, M., & Stoica,, P. (2008). On estimation of covariance matrices with Kronecker product structure. IEEE Transactions on Signal Processing, 56, 479–491.
Wirfält,, P., & Jansson,, M. (2014). On Kronecker and linearly structured covariance matrix estimation. IEEE Transactions on Signal Processing, 62, 1536–1547.