A note on optimal designs in weighted polynomial regression for the classical efficiency functions
نویسنده
چکیده
In this note we consider the D optimal design problem for the heteroscedastic polynomial regression model Karlin and Studden a found explicit solutions for three types of e ciency functions We introduce two new functions to model the heteroscedastic structure for which the D optimal designs can also be found explicitly The optimal designs have equal masses at the roots of generalized Bessel polynomials and Jacobi polynomials with complex parameters It is also demon strated that there exist no other e ciency functions such that the supporting poly nomial of the D optimal design satis es a generalized Rodrigues formula AMS Subject Classi cations Primary K Secondary L
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