Optimal designs for trigonometric and polynomial regression using canonical moments
type: Item
instance of: scholarly article
title: Optimal designs for trigonometric and polynomial regression using canonical moments
zbMATH Open document ID: 0592.62067
author: Tai Shing Lau
author: William J. Studden
published in: The Annals of Statistics
publication date: 1985-01-01T00:00:00Z
review text: The authors construct explicit solutions for the D- and \(D_ s\)-optimal designs of the polynomial regression on \([-1,+1]\) and the trigonometric regression on \([-\pi,+\pi]\). The ideas of using the canonical moments to compute the determinants \(| M|\) or \(| M| /| M_{11}|\) and vice-versa of recovering the design for a specified set of canonical moments are exploited by both authors in their earlier papers; see the second author, ibid. 8, 1132-1141 (1980; Zbl 0447.62070), J. Am. Stat. Assoc. 77, 916-921 (1982; Zbl 0505.62062) and the first author, Theory of canonical moments and its application in polynomial regression. I, II. Tech. Rep. 83-23, 83-24, Purdue Univ. (1983). What is new here is a study of the relationship between the system's cosines and sines and the classical Chebyshev polynomials of 1st and 2nd order presented in section 4, and a study of certain robust designs for these two sets of functions in section 5. The details of the results are too complicated to describe here.
Mathematics Subject Classification ID: 62K05
Mathematics Subject Classification ID: 62J02
Mathematics Subject Classification ID: 62J05
zbMATH DE Number: 3951833
zbMATH Keywords: D sub s optimal designs
zbMATH Keywords: Läuter type optimal designs
zbMATH Keywords: D-optimality
zbMATH Keywords: polynomial regression
zbMATH Keywords: trigonometric regression
zbMATH Keywords: canonical moments
zbMATH Keywords: Chebyshev polynomials
reviewed by: Xuan Loc Nguyen
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aos/1176346599
OpenAlex ID: W2008182816
DOI: 10.1214/AOS/1176346599
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description: scientific article; zbMATH DE number 3951833