OPTIMAL DESIGNS FOR ESTIMATING THE DERIVATIVE IN NONLINEAR REGRESSION

OPTIMAL DESIGNS FOR ESTIMATING THE DERIVATIVE IN NONLINEAR REGRESSION

We consider the problem of estimating the derivative of the expected response in nonlinear regression models. It is demonstrated that in many cases the optimal designs for estimating the derivative have either on m or m − 1 support points, where m denotes the number of unknown parameters in the mode...

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Veröffentlicht in:Statistica Sinica 2011-10, Vol.21 (4), p.1557-1570
Hauptverfasser: Dette, Holger, Melas, Viatcheslav B., Shpilev, Petr
Format: Artikel
Sprache:eng
Schlagworte:
Design efficiency
Experiment design
Linear regression
Mathematical independent variables
Mathematical vectors
Mathematics
Musical intervals
Parametric models
Point estimators
Regression analysis
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Zusammenfassung:We consider the problem of estimating the derivative of the expected response in nonlinear regression models. It is demonstrated that in many cases the optimal designs for estimating the derivative have either on m or m − 1 support points, where m denotes the number of unknown parameters in the model. It is also shown that the support points and weights of the optimal designs are analytic functions, and this result is used to construct a numerical procedure for the calculation of the optimal designs. The results are illustrated in exponential regression and rational regression models.
ISSN:1017-0405
1996-8507
DOI:10.5705/ss.2009.202