On admissibility in various classes of quadratic estimators

Estimation of variance components in several classes of quadratic estimators is considered. It includes estimation with or without unbiasedness and with or without invariance. Relations between sets of admissible estimators in these classes are investigated. It is shown that the set of admissible estimators among (unbiased) invariant quadratics is included in the set of admissible estimators among all (unbiased) quadratics but the set of admissible among all quadratics is disjoint with the set of all unbiased quadratics.