Simulation study on tree-based threshold in generalized Pareto model with the presence of covariate

摘要

Most real life data sets are non-stationary, where they are affected by covariates. The conventional method of modelling non-stationary extremes are by setting a constant high threshold, u where the threshold exceedances are modelled by Generalized Pareto distribution (GPD) and covariates model is incorporated in the GPD parameters to account for the non-stationarity. However, the asymptotic basis of the GPD model might be violated, where threshold u might be high enough for GPD approximation on certain covariates but not on others. In this paper, a covariate-varying threshold selection method based on regression tree is proposed and applied on simulated non-stationary data sets. The tree is used to partition data sets into homogenous groups with similar covariate condition. The uncertainty associated with this threshold selection method is evaluated using the bootstrap procedure. The bootstrap percentile interval obtained is not too wide which conclude that the uncertainty caused by the threshold choice is not too big. Besides, the exceedances of the tree-based threshold can be modelled by stationary GPD model which is simpler than non-stationary model.