## Statistical Science

- Statist. Sci.
- Volume 6, Number 1 (1991), 15-32.

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

#### 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.

#### Article information

**Source**

Statist. Sci. Volume 6, Number 1 (1991), 15-32.

**Dates**

First available in Project Euclid: 19 April 2007

**Permanent link to this document**

http://projecteuclid.org/euclid.ss/1177011926

**Digital Object Identifier**

doi:10.1214/ss/1177011926

**Mathematical Reviews number (MathSciNet)**

MR1108815

**Zentralblatt MATH identifier**

0955.62500

**JSTOR**

links.jstor.org

**Keywords**

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

#### Citation

Robinson, G. K. That BLUP is a Good Thing: The Estimation of Random Effects. Statist. Sci. 6 (1991), no. 1, 15--32. doi:10.1214/ss/1177011926. http://projecteuclid.org/euclid.ss/1177011926.

#### See also

- See Comment: Katherine Campbell. [That BLUP is a Good Thing: The Estimation of Random Effects]: Comment. Statist. Sci., Volume 6, Number 1 (1991), 32--34.Project Euclid: euclid.ss/1177011927
- See Comment: David A. Harville. [That BLUP is a Good Thing: The Estimation of Random Effects]: Comment. Statist. Sci., Volume 6, Number 1 (1991), 35--39.Project Euclid: euclid.ss/1177011928
- See Comment: James C. Spall. [That BLUP is a Good Thing: The Estimation of Random Effects]: Comment: The Kalman Filter and BLUP. Statist. Sci., Volume 6, Number 1 (1991), 39--41.Project Euclid: euclid.ss/1177011929
- See Comment: Terry Speed. [That BLUP is a Good Thing: The Estimation of Random Effects]: Comment. Statist. Sci., Volume 6, Number 1 (1991), 42--44.Project Euclid: euclid.ss/1177011930
- See Comment: Duane Steffey, Robert E. Kass. [That BLUP is a Good Thing: The Estimation of Random Effects]: Comment. Statist. Sci., Volume 6, Number 1 (1991), 45--47.Project Euclid: euclid.ss/1177011931
- See Comment: Robin Thompson. [That BLUP is a Good Thing: The Estimation of Random Effects]: Comment. Statist. Sci., Volume 6, Number 1 (1991), 47--47.Project Euclid: euclid.ss/1177011932
- See Comment: G. K. Robinson. [That BLUP is a Good Thing: The Estimation of Random Effects]: Rejoinder. Statist. Sci., Volume 6, Number 1 (1991), 48--51.Project Euclid: euclid.ss/1177011933