ABSTRACT Dependence measures are often used in practice in order to assess the quality of a regression model. This is for instance the case with Kendall's tau and other association coefficients based on concordance probabilities. However, in case the response variable is discrete, correlation indices are often bounded and restricted to a sub-interval of . Hence, in this context, small positive values of Kendall's tau may actually support goodness of prediction when getting close to its highest attainable value. In this paper, we derive the best-possible upper bounds for Kendall's tau when the response variable is discrete. Two cases are considered, depending on whether the score is continuous or discrete. Also, we illustrate the obtained upper bounds on a motor third-party liability insurance portfolio.

中文翻译：

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离散响应回归模型中基于一致性的预测度量

摘要 在实践中经常使用依赖度量来评估回归模型的质量。例如，基于一致性概率的 Kendall tau 和其他关联系数就是这种情况。然而，在响应变量是离散的情况下，相关指数通常有界并限制在 的子区间内。因此，在这种情况下，当接近可达到的最高值时，肯德尔 tau 的小正值实际上可能支持预测的良性。在本文中，我们推导出响应变量为离散时 Kendall tau 的最佳可能上限。考虑两种情况，具体取决于分数是连续的还是离散的。此外，我们还说明了获得的汽车第三方责任保险组合的上限。