Castilla González, Elena MaríaJaenada Malagón, MaríaMartín Apaolaza, NirianPardo Llorente, Leandro2023-06-222023-06-222022-10-251573-137510.1007/s11222-022-10162-7https://hdl.handle.net/20.500.14352/71935Since 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.engAtribución 3.0 Españajournal articlehttps://doi.org/10.1007/s11222-022-10162-7open access519.22Correlation testInfluence functionRényi pseudodistanceRobustnessWald-type testEstadística matemática (Matemáticas)1209 Estadística