Universal Inference for Testing Calibration of Mean Estimates within the Exponential Dispersion Family
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arXiv
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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866918174808604672 |
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| author | Delong, Łukasz Wüthrich, Mario |
| author_facet | Delong, Łukasz Wüthrich, Mario |
| contents | Calibration of mean estimates for predictions is a crucial property in many applications, particularly in the fields of financial and actuarial decision-making. In this paper, we first review classical approaches for validating mean-calibration, and we discuss the Likelihood Ratio Test (LRT) within the Exponential Dispersion Family (EDF). Then, we investigate the framework of universal inference to test for mean-calibration. We develop a sub-sampled split LRT within the EDF that provides finite sample guarantees with universally valid critical values. We investigate type I error, power and e-power of this sub-sampled split LRT, we compare it to the classical LRT, and we propose a novel test statistics based on the sub-sampled split LRT to enhance the performance of the calibration test. A numerical analysis verifies that our proposal is an attractive alternative to the classical LRT achieving a high power in detecting miscalibration. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_23821 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Universal Inference for Testing Calibration of Mean Estimates within the Exponential Dispersion Family Delong, Łukasz Wüthrich, Mario Applications 62P05 G.3 Calibration of mean estimates for predictions is a crucial property in many applications, particularly in the fields of financial and actuarial decision-making. In this paper, we first review classical approaches for validating mean-calibration, and we discuss the Likelihood Ratio Test (LRT) within the Exponential Dispersion Family (EDF). Then, we investigate the framework of universal inference to test for mean-calibration. We develop a sub-sampled split LRT within the EDF that provides finite sample guarantees with universally valid critical values. We investigate type I error, power and e-power of this sub-sampled split LRT, we compare it to the classical LRT, and we propose a novel test statistics based on the sub-sampled split LRT to enhance the performance of the calibration test. A numerical analysis verifies that our proposal is an attractive alternative to the classical LRT achieving a high power in detecting miscalibration. |
| title | Universal Inference for Testing Calibration of Mean Estimates within the Exponential Dispersion Family |
| topic | Applications 62P05 G.3 |
| url | https://arxiv.org/abs/2510.23821 |