Bayesian and maximin optimal designs for heteroscedastic regression models
نویسندگان
چکیده
The problem of constructing standardized maximin D-optimal designs for weighted polynomial regression models is addressed. In particular it is shown that, by following the broad approach to the construction of maximin designs introduced recently by Dette, Haines and Imhof (2003), such designs can be obtained as weak limits of the corresponding Bayesian Φq-optimal designs. The approach is illustrated for two specific weighted polynomial models and also for a particular growth model.
منابع مشابه
On the number of support points of maximin and Bayesian D-optimal designs in nonlinear regression models
We consider maximin and Bayesian D-optimal designs for nonlinear regression models. The maximin criterion requires the specification of a region for the nonlinear parameters in the model, while the Bayesian optimality criterion assumes that a prior distribution for these parameters is available. It was observed empirically by many authors that an increase of uncertainty in the prior information...
متن کاملOptimal designs for testing the functional form of a regression via nonparametric estimation techniques
For the problem of checking linearity in a heteroscedastic nonparametric regression model under a xed design assumption we study maximin designs which maximize the minimum power of a nonparametric test over a broad class of alternatives from the as sumed linear regression model It is demonstrated that the optimal design depends sensi tively on the used estimation technique i e weighted or ordin...
متن کاملOptimal Weighted Bayesian Design Applied to Dose-response-curve Analysis
Designs for nonlinear regression models depend on some prior information about the unknown parameters. There are three primary methods for accounting for this: The locally optimal designs, globally optimal Bayesian designs, and sequential procedures. If prior knowledge about the parameters is available from former experiments, Bayesian designs integrate this information most eeciently. If the e...
متن کاملA geometric characterization of c-optimal designs for heteroscedastic regression
We consider the common nonlinear regression model where the variance as well as the mean is a parametric function of the explanatory variables. The c-optimal design problem is investigated in the case when the parameters of both the mean and the variance function are of interest. A geometric characterization of c-optimal designs in this context is presented, which generalizes the classical resu...
متن کاملRobustness properties of minimally-supported Bayesian D-optimal designs for heteroscedastic models
Bayesian D-optimal designs supported on a xed number of points were found by Dette and Wong (1998) for estimating parameters in a polynomial model when the error variance depends exponentially on the explanatory variable. This work provides optimal designs under a broader class of error variance structures and investigates the robustness properties of these designs to model and prior distributi...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2011