Optimum estimation in a growth curve model with a priori unknown variance components in geodetic networks. (English) Zbl 0981.86505

Summary: Time varying coordinates of points of geodetic networks are indirectly measured by a group of measurement devices with different characteristics of accuracy in several epochs. The design of the measurement is the same in all epochs. The ratio of the characteristics of accuracy is a priori unknown. The aim is to determine an estimator of the parameters of functions modelling changes of the coordinates, confidence regions of these functions and to construct a procedure for testing linear hypotheses on time varying coordinates of a geodetic network. As the characteristics of accuracy are a priori unknown, the problem of their estimation has to be solved simultaneously. The research of rules of recent crustal movements leads to studying the mentioned model.


86A32 Geostatistics
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[1] Anderson TW (1958) An Introduction to Multivariate Statistical Analysis. J Wiley, New York · Zbl 0083.14601
[2] Janko J (1961) Statistical Tables (in Russian). GOSSTAIZDAT CSU SSSR, Moscow
[3] Koch,KR (1985) Ein statistisches Auswerteverfahren fur Deformationmessungen. Allg. Vermessungsnachrichten 3, pp. 97–108
[4] Kubáček L, Kubáčková L (1986) Statistical aspects of eliminating systematic effects. Studia geoph.et geod.30, pp.1–12
[5] Kubáček L (1988) Foundations of Estimation Theory. Elsevier, Amsterdam-New York-Oxford-Tokyo · Zbl 0698.62004
[6] Kubáček L (1990) Special structures of mixed linear models with nuisance parameters. Math. Slovaca 40, pp.191–207 · Zbl 0745.62071
[7] Kubáček L, Kubáčková L (1992) A statistical approach to studying recent movements. Contr. Geophys. Inst. Slov. Acad. Sci. 22, pp.7–20
[8] Kubáčková L (1986) Collocation with an error component trend. Contr. Geophys. Inst. Slov. Acad. Sci. 19, 7–14
[9] Kubáčková L (1992) The locally best estimator of the first and second order parameters in epoch regression models. Application of Mathematics 37, pp. 1–12 · Zbl 0743.62057
[10] Rao CR (1965) Linear Statistical Inference and Its Applications. J.Wiley, New York · Zbl 0137.36203
[11] Rao CR, Mitra SK (1971) Generalized Inverse of Matrices and Its Applications. J.Wiley, New York · Zbl 0236.15004
[12] Schaffrin B (1983) Varianz – Kovarianz – Komponentenschätzung bei der Ausgleichung heterogener Wiederholungsmessungen. DGK Publ. No C-282, München · Zbl 0541.62052
[13] Schaffrin B (1986) New estimation/prediction techniques for the determination of crustal deformations in the presence of prior geophysical information. Tectonophysics 130, pp.361–367
[14] Srivastava MS, Khatri CG (1979) An Introduction to Multivariate Statistics. North Holland, Amsterdam-New York · Zbl 0421.62034
[15] Žežula I (1994) Covariance components estimation in the growth curve model. Statistics 24, pp. 321–330. · Zbl 0808.62052
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