Confidence regions near singular information and boundary points with applications to mixed models
提出了一种在Fisher信息矩阵奇异时仍能保持渐近正确覆盖率的置信域构造方法，特别适用于混合模型中尺度参数接近或等于零的情形，模拟显示仅需20个观测即可达到近名义覆盖率。
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 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.