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Keywords:
Weakly nonlinear regression model; underparameterization; MSE; BLUE
Weakly nonlinear regression model; underparameterization; MSE; BLUE
Summary:
A large number of parameters in regression models can be serious obstacle for processing and interpretation of experimental data. One way how to overcome it is an elimination of some parameters. In some cases it need not deteriorate statistical properties of estimators of useful parameters and can help to interpret them. The problem is to find conditions which enable us to decide whether such favourable situation occurs.
References:
[1] Bates, D. M., Watts, D. G.: Relative curvature measures of nonlinearity. J. Roy. Stat. Soc. B 42 (1980), 1–25. MR 0567196 | Zbl 0455.62028
[2] Kubáček, L., Kubáčková, L., Volaufová, J.: Statistical Models with Linear Structures. Veda, Bratislava, 1995.
[3] Kubáček, L., Kubáčková, L.: Regression Models with a weak Nonlinearity. Technical Report Nr. 1998.1, Universität Stuttgart, Stuttgart, 1998, 1–67.
[4] Kubáček, L.: Underparametrization in a regression model with constraints II. Math. Slovaca 55 (2005), 579–596. MR 2200144 | Zbl 1150.62390
[5] Kubáček, L.: Underparametrized regression models. Tatra Mt. Math. Publ. 14 (2006), 241–254.
[6] Kubáček, L., Tesaříková, E.: Weakly Nonlinear Regression Models. Vyd. Univerzity Palackého, Olomouc, 2008.
[7] Rao, C. R., Mitra, S. K.: Generalized Inverse of Matrices and its Applications. Wiley, New York–London–Sydney–Toronto, 1971. MR 0338013 | Zbl 0236.15005
[8] Scheffé, H.: The Analysis of Variance. Wiley, New York–London–Sydney, 1967, (fifth printing). MR 1673563
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