Summary
In some nonlinear regression problems with parameterized variance both the design and the method of estimation have to be chosen. We compare asymptotically two methods of estimation: the penalized weighted LS (PWLS) estimator, which corresponds to maximum likelihood estimation (MLE) under the assumption of normal errors, and the two-stage LS (TSLS) estimator. We show that when the kurtosis κ of the distribution of the errors is zero, the asymptotic covariance matrix of the estimator is smaller for PWLS than for TSLS, which may not be the case when κ is not zero. We then suggest to construct two optimum designs, one for PWLS under the assumption κ = 0, the other for TSLS (with arbitrary κ), and compare their properties for different values of κ. All developments are made under the assumption of a randomized design, which allows rigourous proofs for the asymptotic properties of the estimators while avoiding the technical difficulties encountered in classical references such as (1969).
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
H.J. Bierens. Topics in Advanced Econometrics. Cambridge University Press, Cambridge1994.
D. Downing, V.V. Fedorov, and S. Leonov. Extracting information from the variance function: optimal design. In A.C. Atkinson, P. Hackl, and W.G. Müller, editorsmODa6 — Advances in Model-Oriented Design and Analysis, pages 45–52Heidelberg2001. Physica-Verlag.
R.I. Jennrich. Asymptotic properties of nonlinear least squares estimation. Annals of Math. Stat.40:633–6431969.
R.I. Jennrich and M.L. Ralston. Fitting nonlinear models to data. Annals Rev. Biophys. Bioeng.8:195–2381979.
M.B. Malyutov. Design and analysis in generalized regression model F. In V.V. Fedorov and H. Laüter, editorsModel-Oriented Data Analysis, (Eisenach, 1987), volume 297 of Lecture Notes in Econom. and Math. Systems, pages 72–76. Springer, Berlin1988.
J. Stoer and R. Bulirsch. Introduction to Numerical Analysis. Springer, Heidelberg2nd edition1993.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Pázman, A., Pronzato, L. (2004). Simultaneous Choice of Design and Estimator in Nonlinear Regression with Parameterized Variance. In: Di Bucchianico, A., Läuter, H., Wynn, H.P. (eds) mODa 7 — Advances in Model-Oriented Design and Analysis. Contributions to Statistics. Physica, Heidelberg. https://doi.org/10.1007/978-3-7908-2693-7_13
Download citation
DOI: https://doi.org/10.1007/978-3-7908-2693-7_13
Publisher Name: Physica, Heidelberg
Print ISBN: 978-3-7908-0213-9
Online ISBN: 978-3-7908-2693-7
eBook Packages: Springer Book Archive