Extreme Values and Robust Statistics

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In this research, we develop statistical models and tools to gain a better understanding of the extreme behaviour of time series in climate and environmental sciences, and extract information from data when aberrant observations are present. We develop statistical models for the extreme occurrences of temperature, rainfall, etc, that can handle the complex nature of these processes and are able to exploit knowledge that we have about such physical processes at any scale to gain a better comprehension of how the extreme behaviour of these processes has changed, is changing, and is likely to change in the future. There are many other areas that require these types of statistical models, for example: oceanography, hydrology, climatology, reliability, economics, reinsurance, and finance. In short, where inadequate estimates of the frequency and size of extreme occurrences can have a devastating impact, for example: wave heights, water levels, heat waves, structural load, insurance claims, and equity returns. We develop robust dependence estimation methods to understand the dynamics of the time-varying dependence among environmental or energy data which often experience jumps or spikes due to equipment malfunctions or network overloads, among numerous other causes. These robust methods are required in numerous applications as aberrant observations are present in many real-life data sets and they cause classical statistical procedures to yield poor inference. We also develop robust methods to screen the many thousands of explanatory variables available in scientific data so that variable selection or prediction methods can then be applied, and significant relationships ultimately be found. Screening methods are used, for example, to find the genes which are most relevant to a disease or the pixels in an image which are most pertinent to its identification.