Year: 2025
Type: article
Abstract: We define a general method for finding a quasi-best approximant in sup-norm to a target density belonging to a given model, based on independent samples drawn from distributions which average to the target (which does not necessarily belong to the model). We also provide a general method for selecting among a countable family of such models. These estimators satisfy oracle inequalities in the general setting. The quality of the bounds depends on the volume of sets on which |p−q| is close to its maximum, where p,q belong to the model (or possibly to two different models, in the case of model selection). This leads to optimal results in a number of settings, including piecewise polynomials on a given partition and anisotropic smoothness classes. Particularly interesting is the case of the single index model with fixed smoothness β, where we recover the one-dimensional rate: this was an open problem.
Source: Bernoulli
DOI: 10.3150/24-bej1800
Author: Guillaume Maillard
Institution: University of Luxembourg
Language: English
Subfield: Statistics and Probability
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Funder: European Commission
OpenAlex ID: W4283205298