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Focused estimation for noisy and small data sets: a Bayesian minimum expected loss estimator approach
Author(s) -
RamírezHassan Andrés,
CorreaGiraldo Manuel
Publication year - 2019
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/anzs.12271
Subject(s) - frequentist inference , estimator , mathematics , bayesian probability , small area estimation , sample size determination , statistics , minimum variance unbiased estimator , econometrics , bayesian inference
Summary Central to many inferential situations is the estimation of rational functions of parameters. The mainstream in statistics and econometrics estimates these quantities based on the plug‐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 the plug‐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.