Estimation of interclass correlation via a Kotz-type distribution

We estimate interclass (mom–sib) correlation by maximizing the log-likelihood function of a Kotz-type distribution. The results are illustrated on a real life data set due to Galton. Using extensive simulations and the three criteria, namely, bias, MSE and Pitman nearness probability, we compare the proposed estimator with the maximum likelihood estimator based on normal distribution and with a non-iterative estimator due to Srivastava. We conclude that the proposed estimator performs well when the data are not from multivariate normal distribution. However, if the data are from multivariate normal distribution then Srivastava's estimator and normal based maximum likelihood estimator perform well as expected. Testing of hypothesis about this correlation is also discussed using likelihood based tests. It is concluded that score test derived using Kotz-type density performs the best.