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September, 1987 Further Characterizations of Design Optimality and Admissibility for Partial Parameter Estimation in Linear Regression
Norbert Gaffke
Ann. Statist. 15(3): 942-957 (September, 1987). DOI: 10.1214/aos/1176350485

Abstract

The paper gives a contribution to the problem of finding optimal linear regression designs, when only $s$ out of $k$ regression parameters are to be estimated. Also, a treatment of design admissibility for the parameters of interest is included. Previous results of Kiefer and Wolfowitz (1959), Karlin and Studden (1966) and Atwood (1969) are generalized. In particular, a connection to Tchebycheff-type approximation of $\mathbb{R}^s$-valued functions is found, which has been known in case $s = 1$. Strengthened versions of the results are obtained for invariant designs in situations, when invariance properties of the regression setup are available. Applications are given to multiple quadratic regression and to one-dimensional polynomial regression.

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Norbert Gaffke. "Further Characterizations of Design Optimality and Admissibility for Partial Parameter Estimation in Linear Regression." Ann. Statist. 15 (3) 942 - 957, September, 1987. https://doi.org/10.1214/aos/1176350485

Information

Published: September, 1987
First available in Project Euclid: 12 April 2007

zbMATH: 0649.62070
MathSciNet: MR902238
Digital Object Identifier: 10.1214/aos/1176350485

Subjects:
Primary: 62K05
Secondary: 49B40

Rights: Copyright © 1987 Institute of Mathematical Statistics

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Vol.15 • No. 3 • September, 1987
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