We test the hypothesis that simulataneous linear contrasts of multiple variance components equal zero in a Gaussian variance components model via a parametric bootstrap. Applications include but are not limited to nested and crossed designs. The main technical contributions are a computationally efficient decomposition of the normalized residual log-likelihood that does not require the variance components to be non-negative or variance design matrices to be positive semi-definite, a modified Newton method for its minimization, and a method for efficient optimization and sampling under the null hypothesis that certain linear combinations of variance components equal zero. A special case of the proposed procedure is a test for multiple variance components simulataneously equalling zero, for which a likelihood ratio test was not previously available. However, the proposed procedure is significantly more general.

翻译：我们通过参数自助法检验高斯方差分量模型中多个方差分量的同步线性对比是否为零。该方法的适用场景包括但不限于嵌套设计与交叉设计。主要技术贡献包括：一种无需方差分量为非负或方差设计矩阵为半正定的归一化残差对数似然的高效计算分解方法；一种用于最小化该似然的修正牛顿法；以及在特定方差分量线性组合为零的原假设下进行高效优化与抽样的方法。本方法的特例可检验多个方差分量同时为零的情况，而此前似然比检验无法处理此类假设。然而，本方法具有显著的更广泛适用性。