基于Rényi伪距离估计的Wald型检验比较两个相依正态总体的稳健方法
Robust approach for comparing two dependent normal populations through Wald-type tests based on Rényi's pseudodistance estimators
摘要：
自从Fisher（1915，1921）的两篇开创性论文发表以来，二元正态分布在固定值相关系数原假设下的检验就成为一个重要的统计问题。在渐近稳健统计的框架下，它仍然是一个非常感兴趣的研究课题。对于这个和其他测试，专注于配对相关的正常随机样本，Rényi的伪距离估计，建立其渐近分布和迭代算法提供了他们的计算。在此基础上构造了不同问题的Wald型检验统计量，并从理论上研究了它们的影响函数。为了在不同的背景下测试零相关性，广泛的模拟研究和两个基于真实数据的例子支持我们的建议的鲁棒性。
英文摘要：
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, Rényi'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.
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