期刊名称：Sankhya. Series A, mathematical statistics and probability
印刷版ISSN：0976-836X
电子版ISSN：0976-8378
出版年度：2005
卷号：67
期号：04
出版社：Indian Statistical Institute
摘要：The results on optimal designs for diallel crosses are presently available for the standard fixed effects linear model. In some cases, however, parental lines may be randomly selected from a population of lines resulting in a random effects model. Ghosh and Das (2003) discussed $A$-optimal designs in this context for estimation of heritability. In this paper we first propose an unbiased estimator of the ratio of the variance components which has a one-to-one relation with heritability. We then obtain an expression of the variance of this unbiased estimator of the ratio of variance components. Through minimization of the variance we obtain optimal designs and show certain connections with the optimization problem under the fixed effects model.
