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.

翻译：预测中均值估计的校准确立是众多应用领域，尤其是金融与精算决策中的关键性质。本文首先回顾了验证均值校准的经典方法，并讨论了指数散布族内的似然比检验。随后，我们探究了用于检验均值校准的通用推断框架。我们在指数散布族内构建了一种子采样分割似然比检验，该检验通过通用有效临界值提供了有限样本保证。我们研究了该子采样分割似然比检验的第一类错误、检验功效及e-功效，将其与经典似然比检验进行比较，并提出了一种基于子采样分割似然比检验的新检验统计量，以提升校准检验的性能。数值分析证实，我们的方案是经典似然比检验的一种有吸引力的替代方法，在检测误校准方面具有高检验功效。