Natural (Non-)Informative Priors for Skew-symmetric Distributions

TY - JOUR

T1 - Natural (Non-)Informative Priors for Skew-symmetric Distributions

AU - Dette, Holger

AU - Ley, Christophe

AU - Rubio Alvarez, Francisco Javier

PY - 2017/10/10

Y1 - 2017/10/10

N2 - In this paper, we present an innovative method for constructing proper priors for theskewness (shape) parameter in the skew-symmetric family of distributions. The proposed methodis based on assigning a prior distribution on the perturbation effect of the shape parameter, whichis quantified in terms of the total variation distance. We discuss strategies to translate prior beliefsabout the asymmetry of the data into an informative prior distribution of this class. We show via aMonte Carlo simulation study that our non-informative priors induce posterior distributions withgood frequentist properties, similar to those of the Jeffreys prior. Our informative priors yieldbetter results than their competitors from the literature. We also propose a scale-invariant andlocation-invariant prior structure for models with unknown location and scale parameters and pro-vide sufficient conditions for the propriety of the corresponding posterior distribution. Illustrativeexamples are presented using simulated and real data.

AB - In this paper, we present an innovative method for constructing proper priors for theskewness (shape) parameter in the skew-symmetric family of distributions. The proposed methodis based on assigning a prior distribution on the perturbation effect of the shape parameter, whichis quantified in terms of the total variation distance. We discuss strategies to translate prior beliefsabout the asymmetry of the data into an informative prior distribution of this class. We show via aMonte Carlo simulation study that our non-informative priors induce posterior distributions withgood frequentist properties, similar to those of the Jeffreys prior. Our informative priors yieldbetter results than their competitors from the literature. We also propose a scale-invariant andlocation-invariant prior structure for models with unknown location and scale parameters and pro-vide sufficient conditions for the propriety of the corresponding posterior distribution. Illustrativeexamples are presented using simulated and real data.

U2 - 10.1111/sjos.12306

DO - 10.1111/sjos.12306

M3 - Article

SN - 0303-6898

VL - 45

JO - SCANDINAVIAN JOURNAL OF STATISTICS

JF - SCANDINAVIAN JOURNAL OF STATISTICS

IS - 2

ER -