Unbiased risk estimation and scoring rules

TL;DR

This paper extends Stein unbiased risk estimation to broader models and divergence measures, linking it with local proper scoring rules to enhance statistical estimation techniques.

Contribution

It generalizes unbiased risk estimation from Gaussian models to nonparametric densities and from quadratic risks to divergence-based distances, introducing new theoretical connections.

Findings

Extended Stein risk estimation to nonparametric densities

Connected risk estimation with local proper scoring rules

Broadened divergence measures for risk assessment

Abstract

Stein unbiased risk estimation is generalized twice, from the Gaussian shift model to nonparametric families of smooth densities, and from the quadratic risk to more general divergence type distances. The development relies on a connection with local proper scoring rules.