The Annals of Statistics

A New Bound for the Euclidean Norm of the Difference Between the Least Squares and the Best Linear Unbiased Estimators

J. K. Baksalary and R. Kala

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Abstract

A new bound is established for the Euclidean norm of the difference between the least squares estimator and the best linear unbiased estimator of the vector of expectations in the general linear model. The bound is valid regardless of the rank of the dispersion matrix and is expressed in substantially simpler terms than the bounds given earlier by Haberman and by Baksalary and Kala.

Article information

Source
Ann. Statist., Volume 8, Number 3 (1980), 679-681.

Dates
First available in Project Euclid: 12 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aos/1176345018

Digital Object Identifier
doi:10.1214/aos/1176345018

Mathematical Reviews number (MathSciNet)
MR568730

Zentralblatt MATH identifier
0464.62055

JSTOR
links.jstor.org

Subjects
Primary: 62J05: Linear regression

Keywords
Linear model least squares estimator best linear unbiased estimator Euclidean vector norm spectral matrix norm

Citation

Baksalary, J. K.; Kala, R. A New Bound for the Euclidean Norm of the Difference Between the Least Squares and the Best Linear Unbiased Estimators. Ann. Statist. 8 (1980), no. 3, 679--681. doi:10.1214/aos/1176345018. https://projecteuclid.org/euclid.aos/1176345018


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