## The Annals of Statistics

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

#### Abstract

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

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

Dates
First available in Project Euclid: 14 February 2002

https://projecteuclid.org/euclid.aos/1013699990

Digital Object Identifier
doi:10.1214/aos/1013699990

Mathematical Reviews number (MathSciNet)
MR1869237

Zentralblatt MATH identifier
1012.62080

#### Citation

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. https://projecteuclid.org/euclid.aos/1013699990

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