Automated selection of r for stationary and nonstationary models for r largest order statistics

TL;DR

This paper introduces a fast, easy-to-implement goodness-of-fit test based on CCDF for selecting the parameter r in the rGEV model, effective for both small and large samples, and extends it to nonstationary models.

Contribution

It proposes a novel CCDF-based goodness-of-fit test for r selection in rGEV models, improving computational efficiency and applicability to nonstationary data.

Findings

CCDF test performs well for small and large samples

Comparable to existing spacings and entropy difference tests

Extended to nonstationary rGEV models

Abstract

In generalized extreme value model for the r largest order statistics, denoted by rGEV, the selection of r is critical. The existing entropy difference test for selecting r is applicable to large sample. Another existing method (the score test with parametric bootstrap) is applicable to small sample, but computationally demanding. To address this problem for small sample, we propose a new method using a sequence of the goodness-of-fit tests based on the conditional cumulative distribution function (CCDF). The proposed CCDF test is easy to implement and computationally fast. The Cram{\'e}r-von Mises test was employed for the goodness-of-fit purpose. The proposed method is compared via Monte Carlo simulations with existing methods including the spacings, the score, and the entropy difference tests. The proposed CCDF test turned out to perform well for both small and large samples, comparable to the spacings and entropy difference tests. The utility of the proposed method is illustrated by an application to the r largest daily rainfall data in Korea. Additionally, we extended the existing methods and the CCDF test to a nonstationary rGEV model. Wide applicability of the proposed method are discussed.