A note on the asymptotic behavior of the Bernstein estimator of the copula density
| Autor: | Paul Janssen, Noël Veraverbeke, Jan Swanepoel |
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| Jazyk: | angličtina |
| Rok vydání: | 2014 |
| Předmět: |
Statistics and Probability
Statistics::Theory Numerical Analysis Multivariate statistics General theorem Copula (linguistics) Nonparametric statistics Estimator Asymptotic distribution asymptotic normality Bernstein estimator copula density Statistics::Other Statistics Bernstein polynomial Statistics::Computation Joint probability distribution Econometrics Statistics::Methodology Applied mathematics Asymptotic normality Statistics Probability and Uncertainty Mathematics |
| Popis: | Copulas and their corresponding densities are functions of a multivariate joint distribution and the one-dimensional marginals. Bernstein estimators have been used as smooth nonparametric estimators for copulas and copula densities. The purpose of this note is to study the asymptotic distributional behavior of the Bernstein estimator of a copula density. Compared to the existing results, our general theorem does not assume known marginals. This makes our theorem applicable for real data. The work was supported by the IAP Research Network P7/13 of the Belgian State (Belgian Science Policy). The second author thanks the National Research Foundation of South Africa for financial support. The third author acknowledges support from research grant MTM 2008-03129 of the Spanish Ministerio de Ciencia e Innovacion. He is also an extraordinary professor at the North-West University, Potchefstroom, South Africa. |
| Databáze: | OpenAIRE |
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