Optimal Designs for Covariates' Models and Mixed Orthogonal Arrays

Optimum Design for Estimation of Regression Parameters in Multi-Factor Set-Up

“…She restricted investigations in the set-up of completely randomised design (CRD) and studied the nature of optimal allocation of treatments and the values of the covariates in the above set-up for simultaneous estimation of the (fixed) treatment effects and the covariate effects with maximum efficiency in the sense of minimum generalised variance. Subsequently, many authors contributed to this area, namely Wierich (1984), Kurotschka and Wierich (1984), Chadjiconstantinidis and Moyssiadis (1991), Chadjiconstantinidis and Chadjipadelis (1996), Liski et al (2002), Das et al (2003), and Rao et al (2003). Dutta et al (2009a) also considered optimal estimation Downloaded by [University of Connecticut] at 16:44 11 October 2014 of the regression coefficients in the set-ups of split-plot and strip-plot designs where the errors are correlated.…”

“…Furthermore, Dutta et al (2010b) considered D-optimal covariate designs for estimation of regression coefficients in incomplete block design set-up when globally optimal design did not exist. Rao et al (2003) re-visited the problem in completely randomized design (CRD) and randomized block design (RBD) set-ups and for the first time they identified the solution as a mixed orthogonal array (MOA). In this article, the work of Rao et al (2003) has been extended further to the multi-factor set-up and the solutions have been represented through arrays called extended mixed orthogonal arrays (EMOA) which reduce to MOAs in particular cases.…”

“…Rao et al (2003) re-visited the problem in completely randomized design (CRD) and randomized block design (RBD) set-ups and for the first time they identified the solution as a mixed orthogonal array (MOA). In this article, the work of Rao et al (2003) has been extended further to the multi-factor set-up and the solutions have been represented through arrays called extended mixed orthogonal arrays (EMOA) which reduce to MOAs in particular cases. Also, optimum designs have been proposed for the covariate models in nested classification.…”

“…The choice of the values of the covariates for a given set-up ensuring minimum variance for the estimators of the regression parameters has attracted attention in recent times. Rao et al (2003) proposed optimum covariate designs (OCD) through mixed orthogonal arrays for set-ups involving at most two factors where the analysis of variance (ANOVA) effects are orthogonally estimable. In this article, we extended these results and proposed OCDs for the multi-factor set-ups where the factorial effects involving at most t (≤ m) factors are orthogonally estimable.…”

“…In this article, we extended these results and proposed OCDs for the multi-factor set-ups where the factorial effects involving at most t (≤ m) factors are orthogonally estimable. It is seen that optimum designs can be obtained through extended mixed orthogonal arrays (EMOA, Dutta et al, 2009a) which reduce to mixed orthogonal arrays for the particular set-ups of Rao et al (2003). We also proposed constructions of such arrays.…”