Abstract 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.

中文翻译：

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基于期望最大化算法的部分EIV模型的非负方差分量估计

摘要 方差分量估计（VCE）的一个难点是估计可能变成负数，这在实践中是不可接受的。本文介绍了两种针对非负 VCE 的新方法，它们将期望最大化算法用于部分变量误差模型。前者使用不受约束的估计标准搜索所需的解决方案，并在统计上得出结论，当其他现有 VCE 方法实现负估计时，方差分量确实移动到了参数空间的边缘。我们专注于公式化并提供该估计量的非负分析。特别是，后一种方法具有更高的计算效率，将成为现有 VCE 类型算法的实用替代方案。此外，这种方法易于实施，通过引入非负约束自动支持非负方差分量。这两种算法都没有复杂的矩阵求逆并降低了计算复杂度。结果表明，我们的算法可以很好地检索到与其他 VCE 方法相同的估计值，后一种方法可以快速估计参数，并且对于大容量和多源数据处理具有实用性。