Optimal designs for estimating individual coefficients in polynomial regression: A functional approach
نویسندگان
چکیده
In this paper the optimal design problem for the estimation of the individual coe cients in a polynomial regression on an arbitrary interval a b a b is considered Recently Sahm demonstrated that the optimal design is one of four types depending on the symmetry parameter s a b a b and the speci c coe cient which has to be estimated In the same paper the optimal design was identi ed explicitly in three cases It is the basic purpose of the present paper to study the remaining open fourth case It will be proved that in this case the support points and weights are real analytic functions of the boundary points of the design space This result is used to provide a Taylor expansion for the weights and support points as functions of the parameters a and b which can easily be used for the numerical calculation of the optimal designs in all cases which were not treated by Sahm AMS Subject Classi cation Primary K Secondary A
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