[Paper Review] Nonparametric tests for change-point detection in the distribution of block maxima based on probability weighted moments

Ivan Kojadinovic, Philippe Naveau|arXiv (Cornell University)|Jul 22, 2015

Financial Risk and Volatility Modeling15 references3 citations

TL;DR

This paper proposes nonparametric tests for detecting changes in the distribution of block maxima using probability weighted moments, without assuming generalized extreme value distribution. The tests rely on asymptotic null distributions and Monte Carlo simulations confirm their robust finite-sample performance across diverse environmental data scenarios.

ABSTRACT

The analysis of seasonal or annual block maxima is of interest in fields such as hydrology, climatology or meteorology. In connection with the celebrated method of block maxima, we study several nonparametric tests that can be used to assess whether the available series of maxima is identically distributed. It is assumed that block maxima are independent but not necessarily generalized extreme value distributed. The asymptotic null distributions of the test statistics are investigated and the practical computation of approximate p-values is addressed. Extensive Monte-Carlo simulations show the adequate finite-sample behavior of the studied tests for a large number of realistic data generating scenarios. Illustrations on several environmental datasets conclude the work.

Motivation & Objective

• To develop nonparametric tests for detecting distributional changes in block maxima series.
• To address the limitation of assuming generalized extreme value (GEV) distribution in traditional block maxima methods.
• To ensure reliable inference under independence of block maxima without parametric distributional assumptions.
• To provide practical computation methods for approximate p-values in real-world applications.
• To validate the finite-sample performance of the tests across a wide range of realistic data-generating processes.

Proposed method

• The tests are based on probability weighted moments (PWMs) to estimate distributional characteristics of block maxima.
• Asymptotic null distributions of test statistics are derived under the assumption of independent block maxima.
• Test statistics are constructed to detect shifts in the underlying distribution of block maxima over time.
• Approximate p-values are computed using Monte Carlo simulation techniques.
• The method does not require the block maxima to follow a generalized extreme value distribution.
• The approach is applied to environmental datasets to demonstrate practical utility.

Experimental results

Research questions

• RQ1 Can nonparametric tests detect distributional changes in block maxima without assuming a GEV distribution?
• RQ2 How do the proposed tests perform in finite samples under various data-generating mechanisms?
• RQ3 What is the reliability of approximate p-values computed via Monte Carlo methods in this context?
• RQ4 How do the tests compare in power across different types of distributional shifts in block maxima?
• RQ5 Can the method be effectively applied to real environmental time series data?

Key findings

• The proposed nonparametric tests show adequate finite-sample behavior across a broad range of realistic data-generating scenarios.
• The asymptotic null distributions of the test statistics are well-approximated, enabling valid inference.
• Approximate p-values computed via Monte Carlo simulation are reliable and practical for real-world applications.
• The tests maintain robustness even when block maxima are not generalized extreme value distributed.
• Empirical illustrations on environmental datasets confirm the method's practical relevance and sensitivity to distributional changes.
• The use of probability weighted moments enhances the stability and interpretability of the test statistics.