Tree-based threshold model for non-stationary extremes

Many statistical models exist for the extreme values of univariate sequences of independent and identically distributed random variables. However in most applications, especially in environmental study, the data sets are always non-stationary i.e varying systematically in time or with the values of covariates. The ozone data that is considered in this study is an example of the data described. The standard method for modeling the extremes of a non-stationary process is retaining a constant high threshold but incorporate the covariate models into the generalized Pareto distribution parameters. The problem of using a constant high threshold in a standard method is the selected threshold which is sufficiently large for one covariate maybe quite low for the other covariate. In this paper, we proposed an alternative approach that use regression tree to select the threshold. The advantage of using a regression tree is that the ozone data can be partitioned into the homogeneous clusters based on the similar covariate conditions and the constant high threshold can be apply within the resulted clusters.