Article
Full entry |
PDF
(0.3 MB)
Feedback
PDF
(0.3 MB)
Feedback
Keywords:
nonlinear regression model; linearization; constraints of type II
nonlinear regression model; linearization; constraints of type II
Summary:
A linearization of the nonlinear regression model causes a bias in estimators of model parameters. It can be eliminated, e.g., either by a proper choice of the point where the model is developed into the Taylor series or by quadratic corrections of linear estimators. The aim of the paper is to obtain formulae for biases and variances of estimators in linearized models and also for corrected estimators.
References:
[1] D. M. Bates, D. G. Watts: Relative curvature measures of nonlinearity. J. Roy. Statist. Soc. B42 (1980), 1–25. MR 0567196
[2] L. Kubáček, L. Kubáčková, J. Volaufová: Statistical Models with Linear Structures. Veda, Bratislava, 1995.
[3] L. Kubáček: One of the calibration problems. Acta Univ. Palack. Olomuc., Mathematica 36 (1997), 117–130. MR 1620541
[4] L. Kubáček, L. Kubáčková: Regression models with a weak nonlinearity. Technical Report Nr. 1998.1, Universität Stuttgart, 1998, pp. 1–67.
[5] L. Kubáček, L. Kubáčková: Statistics and Metrology. Palacký University in Olomouc–Publishing House, 2000. (Czech)
[6] C. R. Rao: Unified theory of linear estimation. Sankhya A 33 (1971), 371–394. MR 0319321 | Zbl 0236.62048
[7] C. R. Rao: Generalized Inverse of Matrices and Its Applications. J. Wiley, N. York-London-Sydney-Toronto, 1971. MR 0338013 | Zbl 0236.15005
Search
Partner of
