An Inequality for a Measure of Deviation in Linear Models

Thomas Mathew, Kenneth Nordström

Research output: Contribution to journalArticle

2 Citations (Scopus)

Abstract

A matrix inequality is established that provides an upper bound for a quadratic form that involves the difference between two linear unbiased estimators of the same linear parametric function in a general linear model. Various special cases of the inequality are discussed. Certain inequalities that arise in the problem of outlier detection and prediction of observations come out as special cases. In addition, some extensions of Samuelson's inequality are also obtained.

Original languageEnglish
Pages (from-to)344-349
Number of pages6
JournalAmerican Statistician
Volume51
Issue number4
Publication statusPublished - Nov 1997
Externally publishedYes

Keywords

  • Outliers
  • Samuelson's inequality
  • Studentized residuals

ASJC Scopus subject areas

  • Mathematics(all)
  • Statistics and Probability

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  • Cite this

    Mathew, T., & Nordström, K. (1997). An Inequality for a Measure of Deviation in Linear Models. American Statistician, 51(4), 344-349.