标题： 线性混合模型中的统一推断 显示英文标题

标题： Uniform inference in linear mixed models

摘要： 我们为线性混合模型中的推断提供了在参数上一致的有限样本分布近似。 重点在于当现有理论失效的情况下的随机效应方差和协方差，此时它们的协方差矩阵接近或恰好奇异，因此接近或处于参数集的边界。 标准正态密度与得分函数线性组合密度之间的差异的定量界限，例如，可以用于评估足够的样本量。 这些界限还导致了在参数数量和随机效应数量都随着样本量增长的情况下有用的渐近理论。 我们考虑了具有独立聚类的模型以及可能具有发散数量的交叉随机效应的模型，这些模型众所周知很复杂。 模拟表明该理论导致了实际相关的方法。 特别是，所研究的置信区域易于实现，在有限样本中即使某些随机效应的方差接近或等于零，或相关性接近或等于$\pm 1$时，也能达到接近名义上的覆盖率。 显示英文摘要

摘要： We provide finite-sample distribution approximations, that are uniform in the parameter, for inference in linear mixed models. Focus is on variances and covariances of random effects in cases where existing theory fails because their covariance matrix is nearly or exactly singular, and hence near or at the boundary of the parameter set. Quantitative bounds on the differences between the standard normal density and those of linear combinations of the score function enable, for example, the assessment of sufficient sample size. The bounds also lead to useful asymptotic theory in settings where both the number of parameters and the number of random effects grow with the sample size. We consider models with independent clusters and ones with a possibly diverging number of crossed random effects, which are notoriously complicated. Simulations indicate the theory leads to practically relevant methods. In particular, the studied confidence regions, which are straightforward to implement, have near-nominal coverage in finite samples even when some random effects have variances near or equal to zero, or correlations near or equal to $\pm 1$.