Consistency of the likelihood depth estimator for the correlation coefficient

Denecke and Müller (CSDA 55:2724–2738, <CitationRef CitationID="CR2">2011</CitationRef>) presented an estimator for the correlation coefficient based on likelihood depth for Gaussian copula and Denecke and Müller (J Stat Planning Inference 142: 2501–2517, <CitationRef CitationID="CR3">2012</CitationRef>) proved a theorem about the consistency of general estimators based on data depth using uniform convergence of the depth measure. In this article, the uniform convergence of the depth measure for correlation is shown so that consistency of the correlation estimator based on depth can be concluded. The uniform convergence is shown with the help of the extension of the Glivenko-Cantelli Lemma by Vapnik- C̃ ervonenkis classes. Copyright Springer-Verlag Berlin Heidelberg 2014