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Robust designs for polynomial regression by maximizing a minimum of $$D$$- and $$D_1$$-efficiencies. (English) Zbl 1012.62080
Summary: In the common polynomial regression of degree m we determine the design which maximizes the minimum of the $$D$$-efficiency in the model of degree m and the $$D_1$$-efficiencies in the models of degree $$m-j,\dots, m +k$$ $$(j, k\geq 0$$ given). The resulting designs allow an efficient estimation of the parameters in the chosen regression and have reasonable efficiencies for checking the goodness-of-fit of the assumed model of degree $$m$$ by testing the highest coefficients in the polynomials of degree $$m-j,\dots, m +k$$.
Our approach is based on a combination of the theory of canonical moments and general equivalence theory for minimax optimality criteria. The optimal designs can be explicitly characterized by evaluating certain associated orthogonal polynomials.

##### MSC:
 62K05 Optimal statistical designs 33C45 Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.)
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