Open Access
May, 1981 Uniqueness and Eventual Uniqueness of Optimal Designs in Some Time Series Models
R. L. Eubank, Patricia L. Smith, Philip W. Smith
Ann. Statist. 9(3): 486-493 (May, 1981). DOI: 10.1214/aos/1176345453

Abstract

Using the results of Barrow, et al., and Chow on the optimal placement of knots in the approximation of functions by piecewise polynomials, we show the uniqueness or "eventual uniqueness" of optimal designs for certain time series models considered by Sacks and Ylvisaker, and Wahba. In addition, the limiting behavior (as the sample size increases) of the variance of the BLUE of the regression coefficient is characterized in terms of the density defining the design, and the density for the asymptotically optimal design is given.

Citation

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R. L. Eubank. Patricia L. Smith. Philip W. Smith. "Uniqueness and Eventual Uniqueness of Optimal Designs in Some Time Series Models." Ann. Statist. 9 (3) 486 - 493, May, 1981. https://doi.org/10.1214/aos/1176345453

Information

Published: May, 1981
First available in Project Euclid: 12 April 2007

zbMATH: 0511.62086
MathSciNet: MR615425
Digital Object Identifier: 10.1214/aos/1176345453

Subjects:
Primary: 62K05
Secondary: 41A15

Keywords: approximation , optimal design , splines , time series

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 3 • May, 1981
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