Properly recorded estimate and confidence regions obtained by an approximate covariance operator in a special nonlinear model. (English) Zbl 0845.62020

Summary: The properly recorded standard deviation of the estimator and the properly recorded estimate are introduced. Bounds for the locally best linear unbiased estimator and estimate and also confidence regions for a linearly unbiasedly estimable linear functional of unknown parameters of the mean value are obtained in a special structure of nonlinear regression models. A sufficient condition for obtaining the properly recorded estimate in this model is also given.


62F10 Point estimation
62J02 General nonlinear regression
62J05 Linear regression; mixed models
62F25 Parametric tolerance and confidence regions
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[1] W.S. Cleveland: Projection with the wrong inner product and its application to regression with correlated errors and linear filtering of time series. The Annals of Math. Statistics 42 (1971), 616-624. · Zbl 0234.62026
[2] D. Hofmann: Handbuch Messtechnik und Qualitätsicherung. VEB Verlag Technik, Berlin, 1986.
[3] K.M.S. Humak: Statistische Methoden der Modellbildung III. Akademie Verlag, Berlin, 1984. · Zbl 0556.62051
[4] L. Kubáček: Foundations of Estimation Theory. Elsevier, Amsterdam, 1988.
[5] K. Rinner, F. Benz: Jordan/Eggert/Kneissl Handbuch der Vermessungskunde, Band VI. Stuttgart, 1971.
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