On the Best Quadratic Minimum Bias Non-Negative Estimator of a Two-Variance Component Model

Variance components (VCs) in linear adjustment models are usually successfully computed by unbiased estimators. However, for many unbiased VC techniques estimated variance components might be negative, a result that cannot be tolerated by the user. This is, for example, the case with the simple additive VC model aσ2 1 + bσ2 2 with known coefficients a and b, where either of the unbiasedly estimated variance components σ2 1 and σ2 2 may frequently come out negative. This fact calls for so-called non-negative VC estimators. Here the Best Quadratic Minimum Bias Non-negative Estimator (BQMBNE) of a two-variance component model is derived. A special case with independent observations is explicitly presented.