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Uncertainty of the design and covariance matrices in linear statistical model. (English) Zbl 1191.62122

Introduction: Uncertainties in entries of design and covariance matrices influence the variance of estimators and cause their bias. A problem occurs mainly in a linearization of nonlinear regression models, where the design matrix is created by derivatives of some functions. The question is how precise must these derivatives be. Uncertainties of covariance matrices must be suppressed under some reasonable bound as well. The aim of the paper is to give simple rules which enables us to decide how many ciphers an entry of the mentioned matrices must be consisted of.

MSC:

62J05 Linear regression; mixed models
62H12 Estimation in multivariate analysis
62J02 General nonlinear regression
65C60 Computational problems in statistics (MSC2010)

Keywords:

design matrix
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References:

[1] Kubáček, L., Kubáčková, L.: Statistics and Metrology. Vyd. Univ. Palackého, Olomouc, 2000
[2] Rao, C. R.: Linear Statistical Inference and Its Applications. J. Wiley, New York-London-Sydney, 1973 sec. · Zbl 0256.62002
[3] Rao, C. R., Mitra, S. K.: Generalized Inverse of Matrices and its Applications. J. Wiley, New York-London-Sydney-Toronto, 1971. · Zbl 0236.15005
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