Optimal designs for trigonometric and polynomial regression using canonical moments (Q1075729)

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.