|
Abstract:
|
In many applications, it is of interest to estimate an infinite-dimensional parameter, such as a regression function, that can be defined as the minimizer of a population risk. Though there is extensive literature on constructing consistent estimators for infinite-dimensional risk minimizers, there is limited work on quantifying the uncertainty associated with such estimates via, e.g., hypothesis testing and construction of confidence regions. We propose a general inferential framework for infinite-dimensional risk minimizers as a nonparametric extension of the score test, which is commonly employed for likelihood-based inference. We illustrate that our framework requires only mild assumptions and is compatible with a variety of estimation problems. In an example, we specialize our proposed methodology to estimation of regression functions with continuous outcomes.
|
