Bayesian Conditional Mean Estimation in Log-Normal Linear Regression Models with Finite Quadratic Expected Loss

Enrico Fabrizi, Carlo Trivisano

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Log-normal linear regression models are popular in many fields of research. Bayesian estimation of the conditional mean of the dependent variable is problematic as many choices of the prior for the variance (on the log-scale) lead to posterior distributions with no finite moments. We propose a generalized inverse Gaussian prior for this variance and derive the conditions on the prior parameters that yield posterior distributions of the conditional mean of the dependent variable with finite moments up to a pre-specified order. The conditions depend on one of the three parameters of the suggested prior; the other two have an influence on inferences for small and medium sample sizes. A second goal of this paper is to discuss how to choose these parameters according to different criteria including the optimization of frequentist properties of posterior means.
Original languageEnglish
Pages (from-to)1064-1077
Number of pages14
JournalScandinavian Journal of Statistics
Volume43
DOIs
Publication statusPublished - 2016

Keywords

  • efficient estimation
  • generalized hyperbolic distribution
  • generalized inverse Gaussian
  • prior specification

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