Advanced search
Publication Cover
The American Statistician Volume 43, 1989 - Issue 3
Submit an article Journal homepage
119
Views
37
CrossRef citations to date
0
Altmetric
General

The Equality of the Ordinary Least Squares Estimator and the Best Linear Unbiased Estimator

Simo Puntanen Department of Mathematical Sciences, University of Tampere, P.O. Box 607, SF-33101, Tampere, Finland
&
George P. H. Styan Department of Mathematics and Statistics, McGill University, 805 Ouest, Rue Sherbrooke, Montréal, Québec, H3A 2K6, Canada
Pages 153-161 | Received 01 Mar 1986, Published online: 27 Feb 2012
 
Sample our Mathematics & Statistics journals, sign in here to start your FREE access for 14 days

Abstract

It is well known that the ordinary least squares estimator of Xβ in the general linear model E y = Xβ, cov y = σ2 V, can be the best linear unbiased estimator even if V is not a multiple of the identity matrix. This article presents, in a historical perspective, the development of the several conditions for the ordinary least squares estimator to be best linear unbiased. Various characterizations of these conditions, using generalized inverses and orthogonal projectors, along with several examples, are also given. In addition, a complete set of references is provided.

Reprints and Corporate Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

To request a reprint or corporate permissions for this article, please click on the relevant link below:

Order Reprints Request Corporate Permissions

Academic Permissions

Please note: Selecting permissions does not provide access to the full text of the article, please see our help page How do I view content?

Obtain permissions instantly via Rightslink by clicking on the button below:

Request Academic Permissions

If you are unable to obtain permissions via Rightslink, please complete and submit this Permissions form. For more information, please visit our Permissions help page.

Related Research Data

Über monotone Matrixfunktionen
Source: Springer Science and Business Media LLC
When are Gauss-Markov and Least Squares Estimators Identical? A Coordinate-Free Approach
Source: Institute of Mathematical Statistics
Parametric Augmentations and Error Structures under which Certain Simple Least Squares and Analysis of Variance Procedures are Also Best
Source: Informa UK Limited
Linear Statistical Inference and its Applications
Source: John Wiley & Sons, Inc.
LEAST-SQUARES ESTIMATION OF LOCATION AND SCALE PARAMETERS USING ORDER STATISTICS
Source: Oxford University Press (OUP)
Letters to the Editor
Source: Informa UK Limited
On Inference in a General Linear Model with an Incorrect Dispersion Matrix
Source: Springer New York
The theory of least squares when the parameters are stochastic and its application to the analysis of growth curves
Source: JSTOR
On equalities between BLUES, WLSEs, and SLSEs†
Source: Wiley
On Necessary and Sufficient Conditions for Ordinary Least Squares Estimators to Be Best Linear Unbiased Estimators
Source: JSTOR
A Conversation with T. W. Anderson
Source: Institute of Mathematical Statistics
Relationships Between Some Representations of the Best Linear Unbiased Estimator in the General Gauss–Markoff Model
Source: Society for Industrial & Applied Mathematics (SIAM)
LINEAR LEAST SQUARES REGRESSION.
Source: Institute of Mathematical Statistics
Some Relationships between BLUEs, WLSEs and SLSEs
Source: Informa UK Limited
The Coordinate-Free Approach to Gauss-Markov Estimation
Source: Springer Berlin Heidelberg
How Much Do Gauss-Markov and Least Square Estimates Differ? A Coordinate-Free Approach
Source: The Institute of Mathematical Statistics
THE GAUSS-MARKOV THEOREM FOR REGRESSION MODELS WITH POSSIBLY SINGULAR COVARIANCES*
Source: Society for Industrial & Applied Mathematics (SIAM)
Some extensions of the Kantorovich inequality and statistical applications
Source: Elsevier BV
On Canonical Forms, Non-Negative Covariance Matrices and Best and Simple Least Squares Linear Estimators in Linear Models
Source: The Institute of Mathematical Statistics
SERIAL CORRELATION IN REGRESSION ANALYSIS. I
Source: JSTOR
On the minimum efficiency of least squares
Source: Oxford University Press (OUP)
Representations of best linear unbiased estimators in the Gauss-Markoff model with a singular dispersion matrix☆
Source: Published by Elsevier Inc.
The inefficiency of least squares
Source: Oxford University Press (OUP)
Inefficiency and correlation
Source: Oxford University Press (OUP)
On the Estimation of Regression Coefficients in the Case of an Autocorrelated Disturbance
Source: The Institute of Mathematical Statistics
Some Simplifying Results on BLUEs
Source: Informa UK Limited
An extension of a rank criterion for the least squares estimator to be the best linear unbiased estimator
Source: Elsevier BV
Linear Estimation with an Incorrect Dispersion Matrix in Linear Models with a Common Linear Part
Source: Informa UK Limited
Letters to the Editor
Source: Informa UK Limited
On Best Linear Estimation and General Gauss-Markov Theorem in Linear Models with Arbitrary Nonnegative Covariance Structure
Source: Society for Industrial & Applied Mathematics (SIAM)
Distribution of the Circular Serial Correlation Coefficient for Residuals from a Fitted Fourier Series
Source: Institute of Mathematical Statistics
A Necessary and Sufficient Condition That Ordinary Least-Squares Estimators Be Best Linear Unbiased
Source: Informa UK Limited
An Analysis of Variance Test for Normality (Complete Samples)
Source: JSTOR
Multiple Time Series
Source: John Wiley & Sons, Inc.
On the difference between gauss-markov and least squares estimates
Source: Wiley
IV.—On Least Squares and Linear Combination of Observations
Source: Cambridge University Press (CUP)
Criteria for the equality between ordinary least squares and best linear unbiased estimators under certain linear models
Source: Wiley
Approximate Weights
Source: Institute of Mathematical Statistics
Equality of two blues and ridge-type estimates
Source: Informa UK Limited
The inefficiency of least squares: extensions of the kantorovich inequality
Source: Published by Elsevier Inc.
Testing for serial correlation in least squares regression. II.
Source: JSTOR
Comparison of Least Squares and Minimum Variance Estimates of Regression Parameters
Source: The Institute of Mathematical Statistics
Weak generalized inverses and minimum variance linear unbiased estimation
Source: National Institute of Standards and Technology (NIST)

Linking provided by 

Related research

People also read lists articles that other readers of this article have read.

Recommended articles lists articles that we recommend and is powered by our AI driven recommendation engine.

Cited by lists all citing articles based on Crossref citations.
Articles with the Crossref icon will open in a new tab.