A difficulty in variance component estimation (VCE) is that the estimates may become negative, which is not acceptable in practice. This article presents two new methods for non-negative VCE that utilize the expectation maximization algorithm for the partial errors-in-variables model. The former searches for the desired solutions with unconstrained estimation criterion and concludes statistically that the variance components have indeed moved to the edge of the parameter space when negative estimates appear implemented by the other existing VCE methods. We concentrate on the formulation and provide non-negative analysis of this estimator. In particularly, the latter approach, which has greater computational efficiency, would be a practical alternative to the existing VCE-type algorithms. Additionally, this approach is easy to implement, the non-negative variance components are automatically supported by introducing non-negativity constraints. Both algorithms are free from a complex matrix inversion and reduce computational complexity. The results show that our algorithms retrieve well to achieve identical estimates over the other VCE methods, the latter approach can quickly estimate parameters and has practical aspects for the large volume and multisource data processing.
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