1. Optimal Designs for Estimating the Slope of a Polynomial Regression.
- Author
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Murty, V. N. and Studden, W. J.
- Subjects
- *
POLYNOMIALS , *REGRESSION analysis , *ANALYSIS of variance , *APPROXIMATION theory , *EXPERIMENTAL design , *LEAST squares , *OPTIMAL designs (Statistics) , *MATHEMATICAL statistics - Abstract
The problem of estimating the slope of a polynomial regression at a fixed point of the experimental region such that (a) the variance of the least-square estimate of the slope at the fixed point is a minimum and {b) the average variance of the least-square estimate of the slope is a minimum is discussed in this paper. In general these designs can be obtained using Kiefer-Wolfowitz [5] characterization of c-optimal designs, Federov [2] characterization of L-optimal designs, and Studden's [10] generalization of the Elfving Theorem [1]. After presenting a brief review of these characterization theorems, specific illustrations for the quadratic and cubic regressions are presented in detail. [ABSTRACT FROM AUTHOR]
- Published
- 1972
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