Trend detection for heteroscedastic extremes

There are some suggestions that extreme weather events are becoming more frequent due to global warming. From a statistical point of view, this raises the question of trend detection in the extremes of a series of observations. We build upon the heteroscedastic extremes framework by Einmahl et al. (J. R. Stat. Soc. Ser. B. Stat. Methodol. 78(1), 31-51, 2016) where the observations are assumed independent but not identically distributed and the variation in their tail distributions is modeled by the so-called skedasis function. While the original paper focuses on non parametric estimation of the skedasis function, we consider here parametric models and prove the consistency and asymptotic normality of the parameter estimators. A parametric test for trend detection in the case where the skedasis function is monotonic is introduced. A short simulation study shows that the parametric test can be more powerful than the non parametric Kolmogorov-Smirnov type test, even for misspecified models. The methodology is finally illustrated on a dataset of daily maximal temperatures in Fort Collins, Colorado, during the 20th century.