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- W2023928085 abstract "In the polynomial regression model of degree $m in mathbb{N}$ we consider the problem of determining a design for the identification of the correct degree of the underlying regression. We propose a new optimality criterion which minimizes a weighted $p$-mean of the variances of the least squares estimators for the coefficients of $x^l$ in the polynomial regression models of degree $l = 1,cdots, m$. The theory of canonical moments is used to determine the optimal designs with respect to the proposed criterion. It is shown that the canonical moments of the optimal measure satisfy a (nonlinear) equation and that the support points are given by the zeros of an orthogonal polynomial. An explicit solution is given for the discrimination problem between polynomial regression models of degree $m - 2, m - 1$ and $m$ and the results are used to calculate the discrimination designs in the sense of Atkinson and Cox for polynomial regression models of degree $1,cdots,m$." @default.
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- W2023928085 date "1994-06-01" @default.
- W2023928085 modified "2023-10-17" @default.
- W2023928085 title "Discrimination Designs for Polynomial Regression on Compact Intervals" @default.
- W2023928085 doi "https://doi.org/10.1214/aos/1176325501" @default.
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