Title: Data imputation of large observations via Bayesian inference for multivariate extremes
Authors: Simone Padoan - Bocconi University (Italy)
Boris Beranger - University of New South Wales (Australia)
Isadora Antoniano-Villalobos - Ca' Foscari University of Venice (Italy) [presenting]
Abstract: Missing data is a known issue in statistics. In applications placing interest on large observations, usual data imputation methods may fail to reproduce the heavy tail behaviour of the quantities involved. Recent literature has proposed the use of multivariate extreme value theory to predict an unobserved component of a random vector given large observed values of the rest. This is achieved through the estimation of the angular measure controlling the dependence structure in the tail of the distribution. The idea can be extended and used for effective data imputation of multiple components at adequately large levels, provided that the model used for the angular measure is flexible enough to capture complex dependence structures. A Bayesian nonparametric model based on constrained Bernstein polynomials ensures such flexibility while allowing for tractable inference. An additional advantage of this approach is the natural way in which uncertainty about the estimation is incorporated into the imputed values through the Bayesian paradigm.