Hypothesis testing in varying coefficient models for tail index regression

This paper studies the varying coefficient model in tail index regression. The varying coefficient model is known as one of efficient semiparametric model to avoid curse of dimensionality when including the large covariates to the model. Actually, the varying coefficient model is useful in mean, quantile, and other regression. Tail index regression is no exception. On the other hand, 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 is significantly varying with covariate or not. If the effect of non-lineality of the model is weak, the varying coefficient structure reduces to more simpler model, such as constant or zero. Accordingly, hypothesis test for model assessment in varying coefficient model is often discussed in mean and quantile regression, but there are no results in tail index regression yet. In this paper, we study the hypothesis test in varying coefficient models for tail index regression.