Transformation-Kernel Estimation of Copula Densities

The standard kernel estimator of copula densities suffers from boundary biases and inconsistency due to unbounded densities. Transforming the domain of estimation into an unbounded one remedies both problems, but also introduces an unbounded multiplier that may produce erratic boundary behaviors in...

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Bibliographic Details
Published in:Journal of business & economic statistics 2020-01, Vol.38 (1), p.148-164
Main Authors: Wen, Kuangyu, Wu, Ximing
Format: Article
Language:English
Subjects:
Boundary bias
Copula density
Kernel density estimation
Transformation
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Summary:The standard kernel estimator of copula densities suffers from boundary biases and inconsistency due to unbounded densities. Transforming the domain of estimation into an unbounded one remedies both problems, but also introduces an unbounded multiplier that may produce erratic boundary behaviors in the final density estimate. We propose an improved transformation-kernel estimator that employs a smooth tapering device to counter the undesirable influence of the multiplier. We establish the theoretical properties of the new estimator and its automatic higher-order improvement under Gaussian copulas. We present two practical methods of smoothing parameter selection. Extensive Monte Carlo simulations demonstrate the competence of the proposed estimator in terms of global and tail performance. Two real-world examples are provided. Supplementary materials for this article are available online.
ISSN:0735-0015
1537-2707
DOI:10.1080/07350015.2018.1469999