Nonparametric inference and Bayesian computing

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The nonparametrics that I developed (during the period of my previous discovery grant), so far in the context of inference on constrained functions, has shown to work well. The functions of interest here are constrained essentially because they characterize a copula, being for one a distribution function, with uniform margins. Copulas are of fundamental importance because they hold the entire dependency structure between the variates of a random vector, and so they appear naturally in many hypothesis tests. When they are combined with marginals, they become a powerful tool for modelling joint distributions. Much of the inferential methodology for the dependence structure has found concrete applications in many applied sciences, such as genetics and econometrics. The inferential approach is usually frequentist, and in many cases nonparametric. In the latter setup, processes linked to the copula (e.g the Kendall process, or empirical copula process) are the main working tools. These do not usually lead to intrinsic estimators for finite samples, and one often needs to modify them in order to satisfy the constraints, an inconvenience here. Another approach is to construct models by further exploiting the geometry of the problem and providing infinite dimensional models, still remaining tractable. Continuing in this direction, I have two main objectives for the next years.