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\'enyi'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(1915,1921年)对双轨正常分布的无效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;关于这一和其他测试,重点是对等的正常随机样本,提出了R\'enyi的伪远测算器,确定了其无症状分布,并为计算提供了迭代算法;根据这些数据,Wald型测试统计数据针对不同感兴趣的问题,在理论上研究其影响功能;为在不同情况下测试无效相关性,进行了广泛的模拟研究,并用两个基于数据的实际实例来支持我们提案的稳健性。