# Calibration Bands for Mean Estimates within the Exponential Dispersion Family

arXiv: https://arxiv.org/abs/2503.18896 · HTML: https://mlsanity.com/paper/2503.18896/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 7 of its 31 references that are in the map.
- First posted on arXiv 24 Mar 2025.

## Builds on (most cited first, 7 of 7)

- [Regression Diagnostics meets Forecast Evaluation: Conditional Calibration, Reliability Diagrams, and Coefficient of Determination](https://mlsanity.com/paper/2108.03210/) (2021)
- [Autocalibration and Tweedie-dominance for Insurance Pricing with Machine Learning](https://mlsanity.com/paper/2103.03635/) (2021)
- [Generic Conditions for Forecast Dominance](https://mlsanity.com/paper/1805.09902/) (2018)
- [Model Comparison and Calibration Assessment: User Guide for Consistent Scoring Functions in Machine Learning and Actuarial Practice](https://mlsanity.com/paper/2202.12780/) (2022)
- [The Murphy Decomposition and the Calibration-Resolution Principle: A New Perspective on Forecast Evaluation](https://mlsanity.com/paper/2005.01835/) (2020)
- [Honest calibration assessment for binary outcome predictions](https://mlsanity.com/paper/2203.04065/) (2022)
- [Isotonic Recalibration under a Low Signal-to-Noise Ratio](https://mlsanity.com/paper/2301.02692/) (2023)

## Built on by (most cited first, 1 of 1)

- [Assessing model calibration with boosting trees](https://mlsanity.com/paper/2606.08084/) (2026)

## Abstract (arXiv)

A statistical model is said to be calibrated if the resulting mean estimates perfectly match the true means of the underlying responses. Aiming for calibration is often not achievable in practice as one has to deal with finite samples of noisy observations. A weaker notion of calibration is auto-calibration. An auto-calibrated model satisfies that the expected value of the responses for a given mean estimate matches this estimate. Testing for autocalibration has only been considered recently in the literature and we propose a new approach based on calibration bands. Calibration bands denote a set of lower and upper bounds such that the probability that the true means lie simultaneously inside those bounds exceeds some given confidence level. Such bands were constructed by Yang-Barber (2019) for sub-Gaussian distributions. Dimitriadis et al. (2023) then introduced narrower bands for the Bernoulli distribution. We use the same idea in order to extend the construction to the entire exponential dispersion family that contains for example the binomial, Poisson, negative binomial, gamma and normal distributions. Moreover, we show that the obtained calibration bands allow us to construct various tests for calibration and auto-calibration, respectively. As the construction of the bands does not rely on asymptotic results, we emphasize that our tests can be used for any sample size.