On the nonexistence of a global nonnegative minimum bias invariant quadratic estimator of variance components

Sujuan Gao, T. M.F. Smith

Research output: Contribution to journalArticle

2 Scopus citations


We consider nonnegative invariant quadratic estimation of variance components and prove that if there does not exist a nonnegative quadratic unbiased estimator of variance components, there does not exist a nonnegative invariant quadratic estimator with a global minimum bias. The result demonstrates that any nonnegative invariant quadratic estimator can only achieve local minimum bias and explains existing numerical results.

Original languageEnglish (US)
Pages (from-to)117-120
Number of pages4
JournalStatistics and Probability Letters
Issue number2
StatePublished - Nov 1 1995



  • Minimum bias
  • Nonnegative quadratic estimator
  • Variance components

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this