发表机构
University of Florida（佛罗里达大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对线性混合模型中方差-协方差参数，提出基于修正剖面得分统计量的置信区间，在参数接近边界时仍保持接近名义覆盖率，且比通用推断区间窄 1.7 至 3.1 倍。
AI 中文摘要
我们提出了线性混合模型中方差-协方差参数的置信区间，这些区间在兴趣参数或 nuisance 参数接近边界时（即某些随机效应方差较小或强相关时）仍具有接近名义覆盖率的性能。在此类设置下，我们的模拟显示，名义水平为 95% 的标准 Wald、似然比和得分区间覆盖率可低至 45% 或高达 99%，而所提出的区间则接近名义水平。所提出的区间通过反转基于受限似然的修正剖面得分统计量构建，其中 nuisance 参数在扩展参数集上估计。在一项关于自闭症儿童社交化的纵向研究中，随机截距与斜率之间的估计相关性接近负一，我们的区间显示，起始水平较高的儿童改善速度较慢。在一项关于小鼠白细胞计数的遗传学研究中，即使多个区间包含零，我们的区间仍能区分变异类别的贡献。与在有限样本中有效的通用推断区间相比，我们的区间窄 1.7 至 3.1 倍，并且在某个通用区间不有限的情况下是有限的，而计算时间仅为后者的四十七分之一。我们在独立簇和交叉随机效应已知成立的条件下，建立了参数上均匀渐近正确的覆盖率。
英文摘要
We propose confidence intervals with near-nominal coverage of variance-covariance parameters in linear mixed models, even when interest or nuisance parameters are near the boundary, that is, when some random effects have small variances or are strongly correlated. In such settings, our simulations show standard Wald, likelihood ratio, and score intervals with nominal level 95% can have coverage as low as 45% and as high as 99%, while the proposed intervals are near nominal. The proposed intervals invert a modified profile score statistic based on the restricted likelihood, with nuisance parameters estimated on an extended parameter set. In a longitudinal study of socialization in children with autism, where the estimated correlation between the random intercept and slope is near minus one, our intervals show that children who start higher improve more slowly. In a genetic study of white blood cell count in mice, they distinguish the contributions of variant classes even though several intervals include zero. Compared to universal inference intervals, which are valid in finite samples, ours are 1.7 to 3.1 times narrower, and finite where one universal interval is not, at a forty-seventh of the computing time. We establish asymptotically correct coverage uniformly in the parameter under a condition known to hold with independent clusters and crossed random effects.
Comments46 pages, 4 figures
