Hacettepe Journal of Mathematics and Statistics 2651-477X 2651-477X Hacettepe University 10.15672/hujms.464636 Statistics İstatistik Sobolev Convergence of Empirical Bernstein Copulas https://orcid.org/0000-0002-5864-2685 Saekaow Sundusit Chiang Mai University https://orcid.org/0000-0002-7590-5993 Tasena Santi Chiang Mai University 12 08 2019 48 6 1845 1858 09 27 2018 11 01 2019 Copyright © 2002, Hacettepe Journal of Mathematics and Statistics 2002 Hacettepe Journal of Mathematics and Statistics

In this work, we prove that Bernstein estimator always converges to the true copula under Sobolev distances. The rate of convergences is provided in case the true copula has bounded second order derivatives. Simulation study has also been done for Clayton copulas. We then use this estimator to estimate measures of complete dependence for weather data. The result suggests a nonlinear relationship between the dust density in Chiang Mai, Thailand and the temperature and the humidity level.

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