References
- Gauss CF. Theoria Motus Corporum Coelestium. Hamburg: Perthes; 1809. English translation reprinted as Theory of the Motions of the Heavenly Bodies Moving about the Sun in Conic Sections. New York: Dover; 1963.
- Aitken AC. On least squares and linear combinations of observations. Proc Roy Soc Edinburg Sect A. 1935;55: 42–48.
- Watson GS. Linear least squares regression. Ann Math Statist. 1967;38:1679–1699. doi: 10.1214/aoms/1177698603
- Arnold SF. The theory of linear models and multivariate analysis. New York: Wiley; 1981.
- Wilks SS. Sample criteria for testing equality of means, equality of variances, and equality of covariances in a normal multivariate distribution. Ann Math Statist. 1946;17:257–281. doi: 10.1214/aoms/1177730940
- Votaw DF. Testing compound symmetry in a normal multivariate distribution. Ann Math Statist. 1948;19:447–473. doi: 10.1214/aoms/1177730145
- Geisser S. Multivariate analysis of variance for a special covariance case. J Amer Statist Assoc. 1963;58:660–669. doi: 10.1080/01621459.1963.10500876
- Anderson TW. Asymptotic efficient estimation of covariance matrices with linear structure. Ann Statist. 1973;4:227–233.
- Ohlson M, Andrushchenko Z, von Rosen D. Explicit estimators under q-dependence for a multivariate normal distribution. Ann Inst Stat Math. 2011;63:29–42. doi: 10.1007/s10463-008-0213-1
- Rao CR, Kleffe J. Estimation of variance components and applications. Volume 3 of statistics and probability. Amsterdam: North-Holland; 1988.
- Khatri CG. Testing some covariance structures under growth curve model. J Multivariate Anal. 1973;3:102–116. doi: 10.1016/0047-259X(73)90014-6
- Lee JC. Prediction and estimation of growth curves with special covariance structures. J Amer Statist Assoc. 1988;83:432–440. doi: 10.1080/01621459.1988.10478614
- Hu J, Shi S. On the expressions of estimability in testing general linear hypotheses. Comm Statist Theory Methods. 2008;37:782–790. doi: 10.1080/03610920701669868
- Bakaslary JK, Kala R. Criteria for estimability in multivariate linear models. Statistics. 1976;7:5–9.
- Hu J, Liu F, Ahmed SE. Estimation of parameters in the growth curve model via an outer product least squares approach for covariance. J Multivariate Anal. 2012;108:53–66. doi: 10.1016/j.jmva.2012.02.007
- Hu J, Liu F, You J. Estimation of parameters in a generalized GMANOVA model based on analogy and least squares. J Statist Plann Inference. 2012;142:2017–2031. doi: 10.1016/j.jspi.2012.01.022
- Fang KT, Wang SG, von Rosen D. Restricted expected multivariate least squares. J. Multivariate Anal. 2006;97:619–632. doi: 10.1016/j.jmva.2005.03.016
- Monahan JF. A primer on linear models. New York: CRC Press, Taylor and Francis Group; 2008.
- Wong CS. Linear models in a general parametric form. Commun Statist Theory Methods. 1989;18:3095–3115. doi: 10.1080/03610928908830080
- von Neumann J. Some matrix-inequalities and metrization of matrix-space. Tomsk Univ Rev. 1937;1:286–300. Reprinted in Collected Works (Pergamon Press, 1962), iv, 205–219.
- Mirsky L. A trace inequality of John von Neumann. Monatsh Math. 1975;79:303–306. doi: 10.1007/BF01647331
- Eaton ML, Perlman MD. The non-singlularity of generalized sample covariance matrices. Ann Statist. 1973;1:710–717. doi: 10.1214/aos/1176342465