That BLUP is a Good Thing: The Estimation of Random Effects

TLDR

BLUP is a general method for estimating random effects, widely applied in animal breeding, geostatistics, insurance, quality measurement, image denoising, and small‑area estimation, and its study helps clarify fixed versus random effects and bridge Bayesian and classical statistical perspectives. The paper aims to present BLUP theory, illustrate its applications, and discuss its relevance to statistical foundations. The authors develop BLUP theory, provide illustrative applications, and connect it to foundational statistical principles.

Abstract

In animal breeding, Best Linear Unbiased Prediction, or BLUP, is a technique for estimating genetic merits. In general, it is a method of estimating random effects. It can be used to derive the Kalman filter, the method of Kriging used for ore reserve estimation, credibility theory used to work out insurance premiums, and Hoadley's quality measurement plan used to estimate a quality index. It can be used for removing noise from images and for small-area estimation. This paper presents the theory of BLUP, some examples of its application and its relevance to the foundations of statistics. Understanding of procedures for estimating random effects should help people to understand some complicated and controversial issues about fixed and random effects models and also help to bridge the apparent gulf between the Bayesian and Classical schools of thought.