  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.
