Open Access
February, 1991 That BLUP is a Good Thing: The Estimation of Random Effects
G. K. Robinson
Statist. Sci. 6(1): 15-32 (February, 1991). DOI: 10.1214/ss/1177011926


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.


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G. K. Robinson. "That BLUP is a Good Thing: The Estimation of Random Effects." Statist. Sci. 6 (1) 15 - 32, February, 1991.


Published: February, 1991
First available in Project Euclid: 19 April 2007

zbMATH: 0955.62500
MathSciNet: MR1108815
Digital Object Identifier: 10.1214/ss/1177011926

Keywords: Best linear unbiased predition (BLUP) , credibility theory , estimation of random effects , fixed versus random effects , foundations of statistics , Kalman filtering , likelihood , parametric empirical Bayes methods , Ranking and selection , selection index , small-area estimation

Rights: Copyright © 1991 Institute of Mathematical Statistics

Vol.6 • No. 1 • February, 1991
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