Robust designs for polynomial regression by maximizing a minimum
			 of D- and D<sub>1</sub>-efficiencies

Dette, Holger; Franke, Tobias

Robust designs for polynomial regression by maximizing a minimum of D- and D₁-efficiencies

Ann. Statist., Tome 29 (2001) no. 2, p. 1024-1049 / Harvested from Project Euclid

Résumé

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 $m-j,\dots, m +k$ ($j, k\ge 0$ 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.

Publié le : 2001-08-14
Classification: Minimax optimal designs, robust design, D-optimality, D_1-optimality, t-test,, associated orthogonal polynomials, 62K05, 33C45

@article{1013699990,
     author = {Dette, Holger and Franke, Tobias},
     title = {Robust designs for polynomial regression by maximizing a minimum
			 of D- and D<sub>1</sub>-efficiencies},
     journal = {Ann. Statist.},
     volume = {29},
     number = {2},
     year = {2001},
     pages = { 1024-1049},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1013699990}
}

Dette, Holger; Franke, Tobias. Robust designs for polynomial regression by maximizing a minimum
			 of D- and D₁-efficiencies. Ann. Statist., Tome 29 (2001) no. 2, pp.  1024-1049. http://gdmltest.u-ga.fr/item/1013699990/