Constrained nonparametric dependence with application in finance and insurance

In this paper we provide a convenient econometric framework for the analy-sis of nonlinear dependence in financial applications. We introduce models withconstrained nonparametric dependence, which specify the conditional distrib-ution or the copula in terms of a one-dimensional functional parameter. Assuch these models can be viewed as an approach between standard parametricspecifications (which are in general too restrictive) and the fully unrestrictedapproach (which is not well-suited for the interpretation of the patterns of non-linear dependence and suffers from the curse of dimensionality). A natural non-parametric estimator is defined by minimizing a chi-square distance betweenthe constrained densities in the family and an unconstrained kernel estimatorof the density. We derive the asymptotic properties of this estimator and of itslinear functionals. Under an appropriate choice of the functional parameter, theexpected nonparametric one-dimensional rate of convergence of the estimator isobtained. Finally we derive the nonparametric efficiency bound for linear func-tionals and show that the minimum chi-square estimator is nonparametricallyefficient for linear functionals...