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Keywords:
two stage regression models; uncertainty of the type A and B; BLUE; $\mathbf{H}$–optimum estimators
two stage regression models; uncertainty of the type A and B; BLUE; $\mathbf{H}$–optimum estimators
Summary:
This paper is a continuation of the paper [6]. It dealt with parameter estimation in connecting two–stage measurements with constraints of type I. Unlike the paper [6], the current paper is concerned with a model with additional constraints of type II binding parameters of both stages. The article is devoted primarily to the computational aspects of algorithms published in [5] and its aim is to show the power of $\mathbf{H}^*$-optimum estimators. The aim of the paper is to contribute to a numerical solution of the estimation problem in the two stage model, where constraints of type II occur in the second stage.
References:
[1] Kubáček L.: Two stage regression models with constraints. Math. Slovaca 43 (1993), 643–658. MR 1273716
[2] Kubáček L.: Štatistické modely pripojovacích meraní. In. Celoslovenský seminár “Modernizácia geodetických základov Slovenska”, zborník prednášok (ed. M. Petrovič), VÚGK Bratislava, 1993, 28–40.
[3] Kubáček L., Kubáčková L.: Dvouetapové sítě s podmínkami typu I a II. In: Sborník příspěvků spolupracovníků k devadesátinám pana profesora Josefa Vykutila. (Ed. D. Dušátko), Praha–Brno, Vojenský zeměpisný ústav Praha 2002, 58–72.
[4] Kubáčková L.: Foundations of Experimental Data Analysis. : CRC-Press, Boca Raton–Ann Arbor–London–Tokyo. 1992. MR 1244322
[5] Kubáček L., Marek J.: Partial optimum estimator in two stage regression model with constraints and a problem of equivalence. Math. Slovaca 54 (2004), (to appear). MR 2181785 | Zbl 1107.62051
[6] Marek J.: Estimation in connecting measurement. Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math. 43 (2003), 69–86. MR 2056023
[7] Marek J.: Statistical view on measurement in Czech and world literature. (submitted to proceedings of Datastat’03).
[8] Kubáček L., Kubáčková L.: Statistics, Metrology (in Czech). Olomouc. : Publishing House of Palacký University. 2000.
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