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 |
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| container_title | Statistica Sinica |
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| creator | Dette, Holger Melas, Viatcheslav B. Shpilev, Petr |
| description | 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. |
| doi_str_mv | 10.5705/ss.2009.202 |
| format | Article |
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| source | JSTOR Mathematics & Statistics; JSTOR Archive Collection A-Z Listing; EZB-FREE-00999 freely available EZB journals |
| subjects | Design efficiency Experiment design Linear regression Mathematical independent variables Mathematical vectors Mathematics Musical intervals Parametric models Point estimators Regression analysis |
| title | OPTIMAL DESIGNS FOR ESTIMATING THE DERIVATIVE IN NONLINEAR REGRESSION |
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