Best Estimate Reporting with Asymmetric Loss

Abstract

This paper considers the problem of point prediction based on a predictive distribution, representing the uncertainty about the outcome. The issue explored is the reporting of a single characteristic, typically the mean, the median or the mode, in the context of a skewed distribution and asymmetric loss. Special attention is given to the two-piece normal distribution and asymmetric piecewise linear and quadratic loss. The practical context for the issue is the yearly reporting of remaining petroleum resources given by the authorities to stakeholders that may ask for just a single number.