Díaz-García, José A.; Caro-Lopera, Francisco J. Statistical theory of shape under elliptical models via QR decomposition. (English) Zbl 1291.62041 Statistics 48, No. 2, 456-472 (2014). Summary: The statistical shape theory via QR decomposition and based on Gaussian and isotropic models is extended in this paper to the families of non-isotropic elliptical distributions. The new shape distributions are easily computable and then the inference procedure can be studied with the resulting exact densities. An application in Biology is studied under two Kotz models, the best distribution (non-Gaussian) is selected by using a modified Bayesian information criterion (BIC)*. Cited in 1 Document MSC: 62E15 Exact distribution theory in statistics 60E05 Probability distributions: general theory 62H99 Multivariate analysis Keywords:shape theory; maximum likelihood estimators; non-central and non-isotropic shape density; QR decomposition; zonal polynomials PDFBibTeX XMLCite \textit{J. A. Díaz-García} and \textit{F. J. Caro-Lopera}, Statistics 48, No. 2, 456--472 (2014; Zbl 1291.62041) Full Text: DOI References: [1] Fang KT, Zhang YT. Generalized multivariate analysis. Beijing: Science Press, Springer-Verlag; 1990. [2] DOI: 10.1007/978-94-011-1646-6 · doi:10.1007/978-94-011-1646-6 [3] DOI: 10.1214/aos/1176349154 · Zbl 0788.62045 · doi:10.1214/aos/1176349154 [4] Dryden IL, Mardia KV. Statistical shape analysis. Chichester: Wiley; 1998. [5] DOI: 10.2307/1427619 · Zbl 0736.60012 · doi:10.2307/1427619 [6] Goodall CG, J Roy Statist Soc Ser B 53 pp 285– (1991) [7] DOI: 10.1214/aos/1176349259 · Zbl 0831.62003 · doi:10.1214/aos/1176349259 [8] DOI: 10.1016/j.jmva.2004.08.003 · Zbl 1065.62096 · doi:10.1016/j.jmva.2004.08.003 [9] DOI: 10.1016/j.jspi.2005.08.045 · Zbl 1098.62071 · doi:10.1016/j.jspi.2005.08.045 [10] DOI: 10.1090/S0025-5718-06-01824-2 · Zbl 1117.33007 · doi:10.1090/S0025-5718-06-01824-2 [11] DOI: 10.1214/aoms/1177703550 · Zbl 0121.36605 · doi:10.1214/aoms/1177703550 [12] Muirhead RJ, Wiley series in probability and mathematical statistics (1982) [13] DOI: 10.1016/j.jmva.2009.03.004 · Zbl 1177.62069 · doi:10.1016/j.jmva.2009.03.004 [14] DOI: 10.1093/biomet/76.2.271 · Zbl 0666.62056 · doi:10.1093/biomet/76.2.271 [15] DOI: 10.1007/s00357-007-0010-1 · Zbl 1234.62102 · doi:10.1007/s00357-007-0010-1 [16] DOI: 10.1016/0005-1098(78)90005-5 · Zbl 0418.93079 · doi:10.1016/0005-1098(78)90005-5 [17] DOI: 10.1080/01621459.1995.10476572 · doi:10.1080/01621459.1995.10476572 [18] DOI: 10.2307/271063 · doi:10.2307/271063 [19] Davis AW, Multivariate analysis (1980) 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.