Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
Asymptotic efficiency of the two-stage estimation method for copula-based models
Journal of Multivariate Analysis
Statistical Comparisons of Classifiers over Multiple Data Sets
The Journal of Machine Learning Research
Archimedean copula estimation using Bayesian splines smoothing techniques
Computational Statistics & Data Analysis
GeD spline estimation of multivariate Archimedean copulas
Computational Statistics & Data Analysis
Linear B-spline copulas with applications to nonparametric estimation of copulas
Computational Statistics & Data Analysis
GARCH processes with non-parametric innovations for market risk estimation
ICANN'07 Proceedings of the 17th international conference on Artificial neural networks
Efficient estimation of a semiparametric dynamic copula model
Computational Statistics & Data Analysis
An Introduction to Copulas
Inferring parameters and structure of latent variable models by variational bayes
UAI'99 Proceedings of the Fifteenth conference on Uncertainty in artificial intelligence
Nonparametric bivariate copula estimation based on shape-restricted support vector regression
Knowledge-Based Systems
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While parametric copulas often lack expressive capacity to capture the complex dependencies that are usually found in empirical data, non-parametric copulas can have poor generalization performance because of overfitting. A semiparametric copula method based on the family of bivariate Archimedean copulas is introduced as an intermediate approach that aims to provide both accurate and robust fits. The Archimedean copula is expressed in terms of a latent function that can be readily represented using a basis of natural cubic splines. The model parameters are determined by maximizing the sum of the log-likelihood and a term that penalizes non-smooth solutions. The performance of the semiparametric estimator is analyzed in experiments with simulated and real-world data, and compared to other methods for copula estimation: three parametric copula models, two semiparametric estimators of Archimedean copulas previously introduced in the literature, two flexible copula methods based on Gaussian kernels and mixtures of Gaussians and finally, standard parametric Archimedean copulas. The good overall performance of the proposed semiparametric Archimedean approach confirms the capacity of this method to capture complex dependencies in the data while avoiding overfitting.