Discussiones Mathematicae Probability and Statistics 24(2) (2004) 233-253

ESTIMATION IN UNIVERSAL MODELS WITH RESTRICTIONS

Eva Fiserová

Department of Mathematical Analysis and Applied Mathematics
Faculty of Science, Palacký University
Tomkova 40, 779 00 Olomouc, Czech Republic

e-mail: fiserova@inf.upol.cz

Abstract

In modelling a measurement experiment some singularities can occur even if the experiment is quite standard and simple. Such an experiment is described in the paper as a motivation example. It is presented in the papar how to solve these situations under special restrictions on model parameters. The estimability of model parameters is studied and unbiased estimators are given in explicit forms.

Keywords: universal linear model with restrictions, unbiased estimator.

2000 Mathematics Subject Classification: 62J05, 62F10, 62F30.

References

[1]L. Kubácek, L. Kubácková and J. Volaufová, Statistical Models with Linear Structures, Veda, Bratislava 1995.
[2]L. Kubácek and L. Kubácková, Nonsesitiveness regions in universal models, Math. Slovaca 50 (2) (2000), 219-240.
[3]L. Kubácek and L. Kubácková, Statistics and Metrology, VUP, Olomouc 2000 (in Czech).
[4]C.R. Rao and S.K. Mitra, Generalized Inverse of Matrices and its Applications, J. Wiley & Sons, New York, London, Sydney, Toronto 1971.

Received 7 March 2004