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One singular multivariate linear model with nuisance parameters. (English) Zbl 1081.62035

Introduction: There are two approaches in the problem of nuisance parameters in linear models of various structures:
The first one respects the structure of the model and seeks to find classes of linear functionals of useful (main) parameters such that their estimators allow the nuisance parameters to be neglected; the estimators computed under disregarding nuisance parameters remain to be unbiased and efficient. The variance of the estimator belonging to the above mentioned class could behave analogously. The determination of the class having such attributes is of a great importance in practice because the number of nuisance parameters in real situations can be greater than the number of useful parameters.
The second approach solves the problem of nuisance parameters by their elimination by a transformation of the observation vector provided this transformation is not allowed to cause a loss of information on the useful parameters.
The aim this paper is to apply the first approach to one of the multivariate models.

MSC:

62H12 Estimation in multivariate analysis
62J05 Linear regression; mixed models
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References:

[1] Kubáček L., Kubáčková L., Volaufová J.: Statistical Models with Linear Structures. : Veda, Publishing House of the Slovak Academy of Sciences, Bratislava. 1995.
[2] Kubáčková L., Kubáček L.: Elimination Transformation of an Observation Vector preserving Information on the First and Second Order Parameters. Technical Report, No 11, 1990, Institute of Geodesy, University of Stuttgart, 1-71.
[3] Kubáček L., Kubáčková L.: Statistika a metrologie. : Vydavatelství UP, Olomouc. 2000.
[4] Fišerová E., Kubáček L., Kunderová P.: Linear Statistical Models: Regularity, Singularities. : Academia, Praha. in preparation.
[5] Kunderová P.: On one Multivariate linear model with nuisance parameters. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 36 (1997), 131-139. · Zbl 0953.62051
[6] Kunderová P.: Locally best and uniformly best estimators in linear model with nuisance parameters. Tatra Mt. Math. Publ. 22 (2001), 27-36. · Zbl 1001.62021
[7] Kunderová P.: On eliminating transformations for nuisance parameters in multivariate linear model. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 43 (2004), 87-104. · Zbl 1060.62068
[8] Nordström K., Fellman J.: Characterizations and dispersion-matrix robustness of efficiently estimable parametric functionals in linear models with nuisance parameters. Linear Algebra and its Applications 127 (1990), 341-361. · Zbl 0709.62063
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