Since the two seminal papers by Fisher (1915, 1921) were published, the test under a fixed value correlation coefficient null hypothesis for the bivariate normal distribution constitutes an important statistical problem. In the framework of asymptotic robust statistics, it remains being a topic of great interest to be investigated. For this and other tests, focused on paired correlated normal random samples, R\'{e}nyi's pseudodistance estimators are proposed, their asymptotic distribution is established and an iterative algorithm is provided for their computation. From them the Wald-type test statistics are constructed for different problems of interest and their influence function is theoretically studied. For testing null correlation in different contexts, an extensive simulation study and two real data based examples support the robust properties of our proposal.
翻译:自Fisher(1915,1921年)发表两份重要论文以来,根据固定价值相关系数对双轨正常分布的假设无效的假设进行测试是一个重要的统计问题。在无症状的可靠统计数据框架内,这仍然是一个值得调查的主题。对于这个和其他测试,重点是对等的正常随机样本,提出了R\'{e}nyi的假远测算器,建立了它们的无症状分布,并为它们的计算提供了迭代算法。从这些中,Wald型测试统计数据是针对不同感兴趣的问题构建的,其影响功能理论上是研究的。为了在不同情况下测试无效相关性,一项广泛的模拟研究和两个基于真实数据的例子支持我们提案的稳健性。