The use of Jeffreys priors for the Student-t distribution

Abstract

The Jeffreys-rule prior and the marginal independence Jeffreys prior are recently proposed in Fonseca et al. [Objective Bayesian analysis for the Student-t regression model, Biometrika 95 (2008), pp. 325–333] as objective priors for the Student-t regression model. The authors showed that the priors provide proper posterior distributions and perform favourably in parameter estimation. Motivated by a practical financial risk management application, we compare the performance of the two Jeffreys priors with other priors proposed in the literature in a problem of estimating high quantiles for the Student-t model with unknown degrees of freedom. Through an asymptotic analysis and a simulation study, we show that both Jeffreys priors perform better in using a specific quantile of the Bayesian predictive distribution to approximate the true quantile.

Keywords:

• Jeffreys prior
• probability-matching prior
• quantile estimation
• risk management
• Student-t distribution
• value at risk

Acknowledgements

The author would like to thank the editor, the associate editor and the anonymous reviewer for their helpful comments and suggestions that improve the paper.