Structured nonparametric curve estimation - Mammen, Enno (Modern Problems of Stochastic Analysis and Statistics, 2016)
In this note, we discuss structured nonparametric models. Under a structured nonparametric model, we understand a non- or semiparametric model with several nonparametric components where one of the nonparametric components lies in the focus of statistical interest but where all other nonparametric components are nuisance parameters. In structured nonparametrics, the focus of the statistical analysis is inference on this component whereas the goodness of fit of the whole model is only of secondary interest. This creates new challenging problems in the theory of nonparametrics. We will outline this in this note by discussing two classes of models from structured nonparametrics and by highlighting the theoretical questions arising in these classes of models.