Function-valued parameters that can be defined as the minimizer of a population risk arise naturally in many applications. Examples include the conditional mean function and the density function. Although there is an extensive literature on constructing consistent estimators for function-valued risk minimizers, such estimands can typically only be estimated at a slower-than-parametric rate in nonparametric and semiparametric models, and performing calibrated inference can be challenging. In this talk, we present a general inferential framework for function-valued risk minimizers as a nonparametric extension of the classical score test. We demonstrate that our framework is applicable in a wide variety of problems and describe how the approach can be used for inference on a mean regression function under (i) nonparametric and (ii) partially additive models.
About the Speaker
Zoom Participation. See announcement.
Seminars will consist of a 40-minute talk, followed by a 5-10 minute 'discussion' by the speaker's host, and then followed by Q&A.