Sankhya: The Indian Journal of Statistics
2005, Volume 67, Pt. 4, 785--794
Optimal Designs for Estimation of Ratio of Variance Components in Diallel Crosses
Himadri Ghosh, I.A.S.R.I., New Delhi,
Ashish Das, Indian Statistical Institute, New Delhi, India
Chand K. Midha, The University of Akron, Akron, USA
SUMMARY. 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.
AMS (2000) subject classification. 62K10, 62K05.
Key words and phrases. $A$-optimality, variance components, asymptotically unbiased estimator, heritability.