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Sparse M-estimators in semi-parametric copula models

Benjamin PoignardJean-David Fermanian
摘要
We study the large sample properties of sparse M-estimators in the presenceof pseudo-observations. Our framework covers a broad class of semi-parametriccopula models, for which the marginal distributions are unknown and replaced bytheir empirical counterparts. It is well known that the latter modificationsignificantly alters the limiting laws compared to usual M-estimation. Weestablish the consistency and the asymptotic normality of our sparse penalizedM-estimator and we prove the asymptotic oracle property withpseudo-observations, including the case when the number of parameters isdiverging. Our framework allows to manage copula based loss functions that arepotentially unbounded. As additional results, we state the weak limit ofmultivariate rank statistics and the weak convergence of the empirical copulaprocess indexed by such maps. We apply our inference method to copula vinemodels and copula regressions. The numerical results emphasize the relevance ofthis methodology in the context of model misspecifications.
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