Focused estimation for noisy and small data sets: a Bayesian minimum expected loss estimator approach

SummaryCentral to many inferential situations is the estimation of rational functions of parameters. The mainstream in statistics and econometrics estimates these quantities based on theplug ‐in approach without consideration of the main objective of the inferential situation. We propose the Bayesian Minimum Expected Loss (MELO) approach focusing explicitly on the function of interest, and calculating its frequentist variability. Asymptotic properties of the MELO estimator are similar to theplug ‐in approach. Nevertheless, simulation exercises show that our proposal is better in situations characterised by small sample sizes and/or noisy data sets. In addition, we observe in the applications that our approach gives lower standard errors than frequently used alternatives when data sets are not very informative.

Source: Australian and New Zealand Journal of Statistics - August 25, 2019 Category: Statistics Authors: Andr és Ramírez‐Hassan, Manuel Correa‐Giraldo Tags: Original Article Source Type: research