an:06446162
Zbl 1390.62151
Zhigljavsky, Anatoly; Dette, Holger; Pepelyshev, Andrey
A new approach to optimal design for linear models with correlated observations
EN
J. Am. Stat. Assoc. 105, No. 491, 1093-1103 (2010).
00270809
2010
j
62K05 62J05
arcsine distribution; Bickel-Herzberg approach; logarithmic potentials; positive definite functions; singular kernel
Summary: We consider the problem of designing experiments for regression in the presence of correlated observations with the location model as the main example. For a fixed correlation structure approximate optimal designs are determined explicitly, and it is demonstrated that under the model assumptions made by \textit{P. J. Bickel} and \textit{A. M. Herzberg} [Ann. Stat. 7, 77--95 (1979; Zbl 0403.62051)] for the determination of asymptotic optimal design, the designs derived in this article converge weakly to the measures obtained by these authors. {
} We also compare the asymptotic optimal design concepts of \textit{J. Sacks} and \textit{D. Ylvisaker} [Ann. Math. Stat. 37, 66--89 (1966; Zbl 0152.17503); Ann. Math. Stat. 39, 49--69 (1968; Zbl 0165.21505)] and Bickel and Herzberg [loc. cit.] and point out some inconsistencies of the latter. Finally, we combine the best features of both concepts to develop a new approach for the design of experiments for correlated observations, and it is demonstrated that the
resulting design problems are related to the (logarithmic) potential theory.
Zbl 0403.62051; Zbl 0152.17503; Zbl 0165.21505