2021/05/14 by Aaron Hudson, Hudson, Aaron, Marco Carone +3 · 1 citation
Mathematics · #FOS: Computer and information sciences #Methodology (stat.ME) #Statistical Methods and Bayesian Inference #Statistical Methods and Inference #Statistical Methods in Clinical Trials
paper · pdf · doi:10.48550/arxiv.2105.06646
openalex publication_date 2021/05/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
It is often of interest to make inference on an unknown function that is a local parameter of the data-generating mechanism, such as a density or regression function. 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 many cases, these estimands can be expressed as the minimizer of a population risk functional. Here, we propose a general framework that leverages such representation and provides a nonparametric extension of the score test for inference on an infinite-dimensional risk minimizer. We demonstrate that our framework is applicable in a wide variety of problems. As both analytic and computational examples, we describe how to use our general approach for inference on a mean regression function under (i) nonparametric and (ii) partially additive models, and evaluate the operating characteristics of the resulting procedures via simulations.