Likelihood divergence statistics for testing hypotheses in familial data

Renyi Statistics, for testing composite hypotheses in parametric models, are defined as Renyi divergences between unrestricted and restricted estimated joint probability density functions. This family of statistics is proposed to test the equality of intraclass correlation coefficients in multivariate normal familial data. When maximum likelihood estimators are used, asymptotic distributions of test statistics under null hypothesis ate obtained. Renyi statistics are compared with the likelihood ratio test statistic in terms of sizes and powers.