Linear comparative calibration with correlated measurements. (English) Zbl 1135.62059

Summary: The paper deals with the linear comparative calibration problem, i.e., the situation when both variables are subject to errors. Considered is a quite general model which allows to include possibly correlated data (measurements). From the statistical point of view, the model could be represented by a linear errors-in-variables (EIV) model. We suggest an iterative algorithm for estimating the parameters of the analysis function (inverse of the calibration line) and we solve the problem of deriving the approximate confidence regions for the parameters. The confidence limits are derived using the concept of M. G. Kenward and J. H. Roger [Biometrics 53, No. 3, 983–997 (1997; Zbl 0890.62042)]. Their performance is investigated by simulation. The simulation results show that under reasonable restrictions the proposed confidence regions are very satisfactory for practical use.


62J05 Linear regression; mixed models
62F25 Parametric tolerance and confidence regions
62H12 Estimation in multivariate analysis
65C60 Computational problems in statistics (MSC2010)


Zbl 0890.62042
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