奇异信息和边界点附近的置信区域及其在混合模型中的应用
Confidence Regions Near Singular Information and Boundary Points With Applications to Mixed Models
摘要：
我们提出的置信区域具有渐近正确的一致覆盖概率的参数，其Fisher信息矩阵可以是奇异的参数集的重要点。我们的工作的动机是需要可靠的推理尺度参数接近或等于零的混合模型，这是作为一个特殊的情况。置信区域是通过反转由期望信息标准化的分数检验统计量的连续扩展来构造的，我们发现在正则条件下存在于奇异信息点处。类似的结果以前只得到标量参数，条件下比我们强，并没有考虑到混合模型的应用。在模拟中，我们的置信区域具有接近标称的覆盖率，其独立观测值少至$n = 20$，而不管真实参数离边界有多近。这是我们的主要结果的一个推论，建议的检验统计量有一个渐进的χ 2分布的自由度等于测试参数的数量，即使他们的边界上的参数集。
英文摘要：
We propose confidence regions with asymptotically correct uniform coverage probability of parameters whose Fisher information matrix can be singular at important points of the parameter set. Our work is motivated by the need for reliable inference on scale parameters close or equal to zero in mixed models, which is obtained as a special case. The confidence regions are constructed by inverting a continuous extension of the score test statistic standardized by expected information, which we show exists at points of singular information under regularity conditions. Similar results have previously only been obtained for scalar parameters, under conditions stronger than ours, and applications to mixed models have not been considered. In simulations our confidence regions have near-nominal coverage with as few as $n = 20$ independent observations, regardless of how close to the boundary the true parameter is. It is a corollary of our main results that the proposed test statistic has an asymptotic chi-square distribution with degrees of freedom equal to the number of tested parameters, even if they are on the boundary of the parameter set.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
