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

Abstract

The use of covariates in block designs is necessary when the experimental errors cannot be controlled by using only the qualitative factors. 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. 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.