Theoretical Statistics and Mathematics Unit, ISI Delhi

Estimation of ratio of variance components and optimal diallel cross designs

by Ashish Das and Himadri Ghosh

The results on optimal designs for diallel crosses are based on standard linear model assumptions where the general combining ability effects are taken as fixed. Recently Ghosh and
Das (2003) proposed a random effects model that allows one to first estimate the variance
components and then obtain the variances of these estimates. In this paper we first propose an
unbiased estimate of the ratio of the variance components which has a one-to-one relation with
heritability. We then obtain a large sample expression of the variance of this unbiased estimator of the ratio of variance components. Through a simulation study, it is shown that even for
small samples, the large sample variance is close to the exact variance. Through minimization
of the large sample variance we obtain optimal designs and show certain connections with the
optimization problem under the fixed effects model.

isid/ms/2003/10 [fulltext]

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