The Annals of Statistics

Uniqueness and Eventual Uniqueness of Optimal Designs in Some Time Series Models

R. L. Eubank, Patricia L. Smith, and Philip W. Smith

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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.

Article information

Source
Ann. Statist., Volume 9, Number 3 (1981), 486-493.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345453

Digital Object Identifier
doi:10.1214/aos/1176345453

Mathematical Reviews number (MathSciNet)
MR615425

Zentralblatt MATH identifier
0511.62086

JSTOR
links.jstor.org

Subjects
Primary: 62K05: Optimal designs
Secondary: 41A15: Spline approximation

Keywords
Approximation optimal design splines time series

Citation

Eubank, R. L.; Smith, Patricia L.; Smith, Philip W. Uniqueness and Eventual Uniqueness of Optimal Designs in Some Time Series Models. Ann. Statist. 9 (1981), no. 3, 486--493. doi:10.1214/aos/1176345453. https://projecteuclid.org/euclid.aos/1176345453


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