The Annals of Statistics

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

Holger Dette and Tobias Franke

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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.

Article information

Ann. Statist., Volume 29, Number 4 (2001), 1024-1049.

First available in Project Euclid: 14 February 2002

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 62K05: Optimal designs 33C45: Orthogonal polynomials and functions of hypergeometric type (Jacobi, Laguerre, Hermite, Askey scheme, etc.) [See also 42C05 for general orthogonal polynomials and functions]

Minimax optimal designs robust design D-optimality D_1-optimality t-test, associated orthogonal polynomials


Dette, Holger; Franke, Tobias. Robust designs for polynomial regression by maximizing a minimum of D - and D 1 -efficiencies. Ann. Statist. 29 (2001), no. 4, 1024--1049. doi:10.1214/aos/1013699990.

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