FITTING EXTREME VALUE COPULAS WITH UNIMODAL CONVEX POLYNOMIAL REGRESSION USING BERNSTEIN POLYNOMIALS
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Abstract
Bernstein polynomials are suitable for performing shape-constrained regressions, in particular, for unimodal convex regression. The Pickands function is convex and unimodal, being a fundamental element in the theory of extreme value copulas. The purpose of this article is to explain in details the use of Bernstein polynomials in the estimation of Pickands function and to establish a new test of significance for extreme value copulas.
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References
BOYD, S.; VANDENBERGHE, L. Convex optimization. Cambridge university press, 2004.
CHANG, I. S.; CHIEN, L. C.;HSIUNG, C. A.;WEN, C.C.;WU, Y. J. Shape restricted regression with random Bernstein polynomials. In: COMPLEX DATASETS AND INVERSE PROBLEMS. Institute of Mathematical Statistics, 2007. p.187-202.
CORMIER, E.; GENEST, C.; NEŠLEHOVÁ, J. G. Using B-splines for nonparametric inference on bivariate extreme value copulas. Extremes, v.17, n.4, p.633-659, 2014.
JOE, H. Multivariate models and multivariate dependence concepts. CRC Press, 1997.
KADISON, R.V.; LIU, Z., Bernstein Polynomials and Approximation. Available: https://www2.math.upenn.edu/~kadison/bernstein.pdf (accessed 10-13-2021)
NELSEN, R. B. An introduction to copulas. Springer Science & Business Media, 2013.
PICKANDS, J. Multivariate extreme value distributions. In: PROCEEDINGS 43RD SESSION INTERNATIONAL STATISTICAL INSTITUTE. p.859-878, 1981