Title: Sparse estimation within the Pearson system, with an application to financial market risk
Authors: Michelle Carey - Univerity College Dublin (Ireland) [presenting]
Christian Genest - McGill University (Canada)
James Ramsay - McGill University (Canada)
Abstract: Pearson's system is a rich class of models that includes many classical univariate distributions. It comprises all continuous densities arising as solutions to a differential equation involving a vector of parameters. Estimating a Pearson density is challenging as small parameter variations can induce wild changes in the shape of the corresponding density. It is shown how to estimate the parameters and the corresponding density effectively through a penalized likelihood procedure involving differential regularization. The approach combines a penalized regression method and a profiled estimation technique. Simulations and an illustration with S\&P 500 data suggest that this method can improve market risk assessment substantially through value-at-risk and expected shortfall estimates that outperform those currently used by financial institutions and regulators.