Copula parameter estimation by maximum-likelihood and minimum-distance estimators: a simulation study |
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Authors: | Gregor Wei? |
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Institution: | (1) CSIRO, Mathematics, Informatics and Statistics, Locked Bag 17, North Ryde, NSW, 1670, Australia |
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Abstract: | The purpose of this paper is to present a comprehensive Monte Carlo simulation study on the performance of minimum-distance
(MD) and maximum-likelihood (ML) estimators for bivariate parametric copulas. In particular, I consider Cramér-von-Mises-,
Kolmogorov-Smirnov- and L
1-variants of the CvM-statistic based on the empirical copula process, Kendall’s dependence function and Rosenblatt’s probability
integral transform. The results presented in this paper show that regardless of the parametric form of the copula, the sample
size or the location of the parameter, maximum-likelihood yields smaller estimation biases at less computational effort than
any of the MD-estimators. The MD-estimators based on copula goodness-of-fit metrics, on the other hand, suffer from large
biases especially when used for estimating the parameters of archimedean copulas. Moreover, the results show that the bias
and efficiency of the minimum-distance estimators are strongly influenced by the location of the parameter. Conversely, the
results for the maximum-likelihood estimator are relatively stable over the parameter interval of the respective parametric
copula. |
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Keywords: | |
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