Optimal Designs for Best Linear Unbiased Prediction in Diallel Crosses

Most of the available results on optimal block designs for diallel crosses are based on standard linear model assumptions where the general combining ability effects are taken as fixed. In many practical situations, this assumption may not be tenable since often one studies only a sample of inbred lines from a possibly large (hypothetical) population. Recently Ghosh and Das (2003) proposed a random effects model and then estimated the variance components and the variances of these estimates. While comparing the yielding capacities of the cross (i, j), Kempthorne and Curnow (1961) have proposed the estimation of the yielding capacity of any cross based on the least square estimators of the general combining ability effects and/or the mean yield of the cross (i, j). In this paper, the problem of predicting the yielding capacity of the cross (i, j) from the sample of inbred lines has been considered. The properties of the best linear unbiased predictor for predicting the unobserved general combining ability effects together with general mean effect has been studied. We characterize A-optimal complete diallel cross designs and some efficient partial diallel cross designs under this setup.