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.
- Minimum bias
- Nonnegative quadratic estimator
- Variance components
ASJC Scopus subject areas
- Statistics and Probability
- Statistics, Probability and Uncertainty