Change Detection in Climate Extremes

• Activity Number: 24
• Type: Topic Contributed
• Date/Time: Sunday, July 29, 2012 : 2:00 PM to 3:50 PM
• Sponsor: Section on Statistics and the Environment
• Author(s): Ying Lu*+
• Companies: University of Minnesota-Twin Cities
• Keywords: CUSUM ; extreme value distribution ; likelihood ratio ; hurricane

Abstract

In many modern applications of Statistics, the data arrives in a sequential order, and the question of interest is whether the parameters of the data generating system have remained stable through the entire time-length of data collection. In the setting where data come from an extreme value distribution, we construct a likelihood ratio test statistic to study the stability of parameters and study the effectiveness of using our distribution-specific test statistic, as opposed to the normality-driven CUSUM statistic. The conclusion is that when the underlying distribution belongs to the extreme value distribution family, our likelihood-ratio statistic generally works better than the normal CUSUM statistic, especially when the potential change in parameters is small in size. Two measures have been proposed to evaluate the performance of the two methodologies, namely the average run length and p-value. Finally, we conduct a detailed study on the extreme wind speed and extreme central pressure for the Atlantic hurricane over the past 58 years, and the validity of our methodology is strengthened.