Ranking of PBIBD's with Regard to A-Optimality Criterion Under A Mixed Model

Abstract

For the problem of estimation of all elementary treatment contraata, restrictina ourselves to PBIBD's with two clus association schemea under a mixed model we follow the approach of Sinha and Sinha (1969) to study the behaviour of tho average variance $\overline{v}$ as a function of $\theta ={\lambda }_1-{\lambda }_2$ and also as a function of the auociation scheme to some extent. The functional form of $\overline{v}$ turna out to be the Jame as that under fixed effects model and either $\overline{V(}\theta )⩽\overline{V}(-\theta )\hspace{0.17em}\text{Or}\hspace{0.17em}\overline{V(}\theta )⩾\overline{V}(-\theta )$ for all admissible θ>0. We got that when a BIB dosian does not exist with tho alven parameters a GO design with ${\lambda }_2={\lambda }_1+1,$ if it exists, is A-optimal within the class of all PBIB designs with two associate class association schemes. This proves that in respect of A-optimality, the result of Chong (1978) can be extended to all GD designs with ${\lambda }_2={\lambda }_1+1,$ if we restrict ourselves to such PBIB dosigns.