D-optimal designs for covariate models. (English) Zbl 1462.62478
Summary: The problem of finding D-optimal designs in the presence of a number of covariates has been considered in the one-way set-up. This is an extension of A. Dey and R. Mukerjee [Statistics 40, No. 4, 297–305 (2006; Zbl 1098.62100)] in the sense that for fixed replication numbers of each treatment, an alternative upper bound to the determinant of the information matrix has been found through completely symmetric C-matrices for the regression coefficients; this upper bound includes the upper bound given in [loc. cit.] obtained through diagonal C-matrices. Because of the fact that a smaller class of C-matrices was used at the intermediate stage where the replication numbers were fixed, ultimately some optimal designs remained unidentified there. These designs have been identified here and thereby the conjecture made in [loc. cit.] has been settled.
Citations:
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