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Uniform in bandwidth consistency for the transformation kernel estimator of copulas
Cheikh Tidiane Seck, Diam Ba, Gane Samb Lo · 2016-12-29 · via math.ST updates on arXiv.org

In this paper we establish the uniform in bandwidth consistency for the transformation kernel estimator of copulas introduced in [Omelka et al.(2009)]. To this end, we first prove a uniform in bandwidth law of the iterated logarithm for the maximal deviation of this estimator from its expectation. We then show that, as n goes to infinity, the bias of the estimator converges to zero uniformly in the bandwidth h, varying over a suitable interval. A practical method of selecting the optimal bandwidth is also presented. Finally, we make conclusive simulation experiments showing the performance of the estimator in finite samples.

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