OPTIMAL DESIGNS ON TCHEBYCHEFF POINTS,
Abstract
Kiefer and Wolfowitz (1959) proved that the optimal design for estimating the highest coefficient in polynomial regression is supported by certain Tchebycheff points. Hoel and Levine (1964) showed that the optimal designs for extrapolation in polynomial regression were all supported by the Tchebycheff points. These results were extended by Kiefer and Wolfowitz (1965) to cover nonpolynomial regression problems involving Tchebycheff systems and the large class of designs supported by the Tchebycheff points was characterized. In the present paper it is shown that the optimal design for estimating any specific parameter is supported by one of two sets of Tchebycheff points. Different proofs of the Kiefer-Wolfowitz results are also presented. (Author)
Document Details
- Document Type
- Technical Report
- Publication Date
- Sep 01, 1967
- Accession Number
- AD0659064
Entities
People
- William J. Studden
Organizations
- Purdue University