Tail single-index regression with locally stationary regressors

In extreme value theory, the tail index parameter controls the tail behavior of a distribution function and is thus of primary interest in analyzing extreme events. Recent developments in modeling the tail index along with covariates have been in semi-parametric regression, but there is a lack of flexible models for time series data, especially for non stationary data. To handle such cases, this article proposes a novel tail single-index regression model incorporating locally stationary covariates to address time-varying tail behaviors. For the proposed model, we develop an estimation procedure by proposing an iterative algorithm and a selection method for the tuning parameter. The asymptotic properties of the estimators are constructed in the time-dependent context. Numerical studies and an analysis of Ozone data demonstrate the effectiveness of our model and corresponding theories.