A0677
Title: Nonparametric heavy-tailed distribution estimation via random probability measures
Authors: Carlotta Pacifici - Bocconi University (Italy) [presenting]
Simone Padoan - Bocconi University (Italy)
Stefano Rizzelli - University of Padova (Italy)
Abstract: Estimating the distribution that has generated the observed data is particularly challenging in the case of heavy tails. This task is addressed by focusing on three key objectives: Avoiding strong modeling assumptions, accurately capturing the upper-tail behavior, and allowing for uncertainty quantification. A Bayesian nonparametric framework is adopted, using the Pitman-Yor process (PYP) for estimating the unknown data-generating distribution. Unlike the Dirichlet process, the PYP preserves heavy tails when centered on a heavy-tailed base measure, the same holds for the posterior process. It is sampled from the posterior PYP that combines information from the observed data and the prior base measure, resulting in multiple trajectories that aim to mimic the sample distribution. Simulation studies show coherence between the sampled trajectories and the true one when the base measure matches the true model. Since the data-generating process is unknown in practice, as base measure, a piecewise density is specified with a generalized Pareto upper tail. The resulting trajectories capture the true tail index and yield good coverage at both low and high portions of the distribution.
