Hypothesis testing for varying coefficient models in tail index regression

TL;DR

This paper develops a hypothesis testing framework for assessing whether the coefficient functions in varying coefficient models are constant or vary with covariates specifically in tail index regression, addressing a gap in existing methods.

Contribution

It introduces an asymptotic theory and a hypothesis testing procedure for the varying coefficient model in tail index regression, which was previously unexplored.

Findings

The proposed test effectively detects non-constant coefficient functions.

Asymptotic properties of the estimator are established.

The method is applicable to high-dimensional covariates.

Abstract

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.