Tail Classification using Non-Linear Regression on Tail Model Plots

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Abstract
Selecting an appropriate statistical model is a crucial initial step in various statistical analyses, particularly when estimating extreme values. Empirical plots, such as Pareto, log-normal, and Weibull plots, serve as valuable tools for visualizing the data and identifying patterns that can suggest a suitable model. In classical extreme value methodology, tail modeling often relies on linear regression applied to the upper quantiles or probability plots. Focusing on probability plots, we extend the traditional linear regression approach to encompass non-linear regression. This expansion enables the visualization of extreme data in terms of their compatibility with widely accepted tail models. We then develop asymptotic theory for the non-linearity parameter, which, in turn, allows us to formalize classification procedures to distinguish between specific sets of tail models.