Exploratory data analysis of extreme values using non-parametric kernel methods

In environmental fields such as climatology or hydrology the study of extreme events (e.g. heat waves, storms, floods) is of high importance. These extreme events are those whose observed values exceed a threshold and lie in the tails of the distribution function. We investigate some non-parametric methods to analyze these tail distributions by introducing a modification of classical kernel estimators which focuses directly on the tail density. Given the mild distributional assumptions required to compute these kernel estimators, we can consider them to be the closest smooth representation of the discretized data sample. This allows us to visualize the tail behavior without the gaps in the observed data and without having to impose the stronger assumptions of a parametric model. In more quantitative terms, computing the divergences of a suite of parametric models to the kernel tail density estimator serves as a proxy for selecting which of these parametric models most closely fits the data sample. Moreover our proposed approach, being kernel-based, is straightforward to extend to the exploratory analysis of multivariate extremes. We illustrate the applicability of our non-parametric analysis on a range of simulated and experimental environmental extreme values data.

Jun 15, 2015