期刊
JOURNAL OF MULTIVARIATE ANALYSIS
卷 166, 期 -, 页码 160-181出版社
ELSEVIER INC
DOI: 10.1016/j.jmva.2018.03.002
关键词
Donsker class; Empirical copula process; Local linear estimator; Pair-copula construction; Partial copula; Smoothing; Weak convergence
资金
- Fonds de la Recherche Scientifique Belgium (FRS-FNRS) [A4/5 FC 2779/2014-2017, 22342320]
- Communaute francaise de Belgique [12/17-045]
- IAP research network Grant of the Belgian government (Belgian Science Policy) [P7/06]
A common assumption in pair-copula constructions is that the copula of the conditional distribution of two random variables given a covariate does not depend on the value of that covariate. Two conflicting intuitions arise about the best possible rate of convergence attainable by nonparametric estimators of that copula. On the one hand, the best possible rates for estimating the marginal conditional distribution functions are slower than the parametric one. On the other hand, the invariance of the conditional copula given the value of the covariate suggests the possibility of parametric convergence rates. The more optimistic intuition is shown to be correct, confirming a conjecture supported by extensive Monte Carlo simulations by Hobxk Haff and Segers (2015) and improving upon the nonparametric rate obtained theoretically by Gijbels et al. (2015). The novelty of the proposed approach lies in a double smoothing procedure for the estimator of the marginal conditional distribution functions. The copula estimator itself is asymptotically equivalent to an oracle empirical copula, as if the marginal conditional distribution functions were known. (C) 2018 Elsevier Inc. All rights reserved.
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