Galton, Stein and empirical Bayes: artefacts and connections

Abstract

The problem of fallible data ('errors-in-variables') is traced back to Galton's original discovery of 'regression'. Galton's regression is nothing more than the statistical artefact associated with the well known bias of least squares. The interconnections of Galtonts regression, errors-in-variables, Stein-rule estimation, psychometric test theory, least squares, 'permanent income hypothesis', reliability and empirical Bayes are investigated. This essay discusses how a hybrid solution for fallible observation, Stein-rule least squares, can help to improve our understanding of diverse statistical approaches and problems and why the reliability of our data needs to be explicitly incorporated into our empirical estimates.