×

Multivariate statistical models; solvability of basic problems. (English) Zbl 1228.62067

Summary: Multivariate models frequently used in many branches of science have a relatively large number of different structures. Sometimes the regularity conditions which enable us to solve statistical problems are not satisfied and it is reasonable to recognize them in advance. In this paper a model without constraints on the parameters is analyzed only, since the amount of the class of such problems in general is out of the size of the paper.

MSC:

62H12 Estimation in multivariate analysis
62H05 Characterization and structure theory for multivariate probability distributions; copulas
62J05 Linear regression; mixed models
PDF BibTeX XML Cite
Full Text: EuDML

References:

[1] Anderson, T. W.: An Introduction to Multivariate Statistical Analysis. Wiley, New York, 1958. · Zbl 0083.14601
[2] Fišerová, E., Kubáček, L.: Insensitivity regions for deformation measurement on a dam. Environmetrics 20 (2009), 776-789.
[3] Fišerová, E., Kubáček, L., Kunderová, P.: Linear Statistical Models: Regularity and Singularities. Academia, Praha, 2007.
[4] Fišerová, E., Kubáček, L.: Sensitivity analysis in singular mixed linear models with constraints. Kybernetika 39 (2003), 317-332. · Zbl 1248.62112
[5] Fišerová, E., Kubáček, L.: Statistical problems of measurement in triangle. Folia Fac. Sci. Nat. Univ. Masarykianae Brunensis, Mathematica 15 (2004), 77-94. · Zbl 1134.62340
[6] Giri, N. G.: Multivariate Statistical Analysis. Marcel Dekker, New York-Basel, 2004) · Zbl 1047.62048
[7] Kshirsagar, A. M.: Multivariate Analysis. Marcel Dekker, New York-Basel, 1972. · Zbl 0246.62064
[8] Kubáček, L.: Statistical models of a priori and a posteriori uncertainty in measured data. Proceedings of the MME’95 Symposium, Selected papers of the international symposium, September 18-20, (Eds. Hančlová, J., Dupačová, J., Močkoř, J., Ramík, J.), VŠB-Technical University, Faculty of Economics, Ostrava, 1995, 79-87.
[9] Kubáček, L.: Criterion for an approximation of variance components in regression models. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Mathematica 34 (1995), 91-108. · Zbl 0852.62063
[10] Kubáček, L.: Linear model with inaccurate variance components. Applications of Mathematics 41 (1996), 433-445. · Zbl 0870.62056
[11] Kubáček, L.: On an accuracy of change points. Math. Slovaca 52 (2002), 469-484. · Zbl 1014.62022
[12] Kubáček, L.: Multivariate Statistical Models Revisited. Vyd. University Palackého, Olomouc, 2008.
[13] Kubáček, L., Fišerová, E.: Problems of sensitiveness and linearization in a determination of isobestic points. Math. Slovaca 53 (2003), 407-426. · Zbl 1070.62057
[14] Kubáček, L., Fišerová, E.: Isobestic points: sensitiveness and linearization. Tatra Mt. Math. Publ. 26 (2003), 1-10. · Zbl 1065.62118
[15] Kubáček, L., Kubáčková, L.: The effect of stochastic relations on the statistical properties of an estimator. Contr. Geophys. Inst. Slov. Acad. Sci. 17 (1987), 31-42.
[16] Kubáček, L., Kubáčková, L.: Sensitiveness and non-sensitiveness in mixed linear models. Manuscripta Geodaetica 16 (1991), 63-71.
[17] Kubáček, L., Kubáčková, L.: Unified approach to determining nonsensitiveness regions. Tatra Mt. Math. Publ. 17 (1999), 1-8. · Zbl 0986.62052
[18] Kubáček, L., Kubáčková, L.: Nonsensitiveness regions in universal models. Math. Slovaca 50 (2000), 219-240. · Zbl 0984.62040
[19] Kubáček, L., Kubáčková, L.: Statistical problems of a determination of isobestic points. Folia Fac. Sci. Nat. Univ. Masarykianae Brunensis, Mathematica 11 (2002), 139-150. · Zbl 1046.62067
[20] Kubáček, L., Kubáčková, L., Tesaříková, E., Marek, J.: How the design of an experiment influences the nonsensitiveness regions in models with variance components. Application of Mathematics 43 (1998), 439-460. · Zbl 0937.62070
[21] Kubáčková, L., Kubáček, L.: Optimum estimation in a growth curve model with a priori unknown variance components in geodetic networks. Journal of Geodesy 70 (1996), 599-602. · Zbl 0981.86505
[22] Kubáčková, L., Kubáček, L., Bognárová, M.: Effect of the changes of the covariance matrix parameters on the estimates of the first order parameters. Contr. Geophys. Inst. Slov. Acad. Sci. 20 (1990), 7-19.
[23] Rao, C. R.: Least squares theory using an estimated dispersion matrix and its application to measurement in signal. Proc. 5th Berkeley Symposium on Mathematical Statistics and Probability, Vol 1., Theory of Statistics, University of California Press, Berkeley-Los Angeles, 1967, 355-372.
[24] Seber, G.: Multivariate Observations. Wiley, Hoboken, New Jersey, 2004. · Zbl 0627.62052
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. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.