T-calibration in semi-parametric models

TL;DR

This paper explores the concept of calibration in semi-parametric models, linking it to the existence of a universally optimal parameter across all consistent loss functions, thereby providing a theoretical characterization.

Contribution

It establishes a theoretical equivalence between model calibration and the existence of a parameter optimal under all consistent loss functions in semi-parametric models.

Findings

Calibration corresponds to a parameter optimal under all consistent loss functions

Provides a theoretical criterion for calibration in semi-parametric models

Links calibration to the concept of consistent loss functions

Abstract

This note relates the calibration of models to the consistent loss functions for the target functional of the model. We demonstrate that a model is calibrated if and only if there is a parameter value that is optimal under all consistent loss functions.