A0971
Title: Nonparametric assessment of conditional dependence using a restricted score test
Authors: Aaron Hudson - Unviersity of California, Berkeley (United States) [presenting]
Abstract: Infinite-dimensional parameters that can be defined as the minimizer of a population risk arise naturally in many applications. Classic examples include the conditional mean function and the density function. 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. We illustrate that our framework requires only mild assumptions and is applicable to a variety of estimation problems. As an example, we apply our proposed methodology to test for conditional dependence in a graphical model for which the conditional mean of any node given all remaining nodes takes an arbitrary additive form.
