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Since the two seminal papers by Fisher (1915, 1921) were published, the testunder a fixed value correlation coefficient null hypothesis for the bivariatenormal distribution constitutes an important statistical problem. In theframework of asymptotic robust statistics, it remains being a topic of greatinterest to be investigated. For this and other tests, focused on pairedcorrelated normal random samples, R\'{e}nyi's pseudodistance estimators areproposed, their asymptotic distribution is established and an iterativealgorithm is provided for their computation. From them the Wald-type teststatistics are constructed for different problems of interest and theirinfluence function is theoretically studied. For testing null correlation indifferent contexts, an extensive simulation study and two real data basedexamples support the robust properties of our proposal.

Robust approach for comparing two dependent normal populations through Wald-type tests based on R\'enyi's pseudodistance estimators