This study examines the varying coefficient model in tail index regression. The varying coefficient model is an efficient semiparametric model that avoids the curse of dimensionality when including large covariates in the model. In fact, the varying coefficient model is useful in mean, quantile, and other regressions. The tail index regression is not an exception. However, the varying coefficient model is flexible, but leaner and simpler models are preferred for applications. Therefore, it is important to evaluate whether the estimated coefficient function varies significantly with covariates. If the effect of the non-linearity of the model is weak, the varying coefficient structure is reduced to a simpler model, such as a constant or zero. Accordingly, the hypothesis test for model assessment in the varying coefficient model has been discussed in mean and quantile regression. However, there are no results in tail index regression. In this study, we investigate the asymptotic properties of an estimator and provide a hypothesis testing method for varying coefficient models for tail index regression.

翻译：本研究探讨尾指数回归中的变系数模型。变系数模型是一种有效的半参数模型，当模型中包含大量协变量时，能够避免维数灾难。事实上，变系数模型在均值回归、分位数回归及其他回归中均有广泛应用，尾指数回归亦不例外。然而，尽管变系数模型具有灵活性，但在实际应用中更倾向于使用更简洁、更简单的模型。因此，评估估计的系数函数是否随协变量显著变化至关重要。若模型非线性效应较弱，变系数结构可简化为更简单的模型（如常数模型或零模型）。相应地，均值回归和分位数回归中已讨论了用于变系数模型评估的假设检验方法，但尾指数回归领域尚无相关成果。本研究中，我们考察了估计量的渐近性质，并提出了适用于尾指数回归中变系数模型的假设检验方法。