Second-order properties of intraclass correlation estimators for a symmetric normal distribution

Consider the problem of estimating the intraclass correlation coefficient of a symmetric normal distribution under the squared error loss function. The general admissibility of the standard estimators of the intraclass correlation coefficient is hard to check due to their complicated sampling distributions. We follow the asymptotic decision-theoretic approach of Ghosh and Sinha (1981) and prove that the three standard intraclass correlation estimators (the maximum-likelihood estimator, the method-ofmoments estimator and the first-order unbiased estimator) are second-order admissible for all p >= 2, p being the dimension of the distribution.