Inference about a scalar parameter of interest typically relies on the asymptotic normality of common likelihood pivots, such as the signed likelihood root, the score and Wald statistics. Nevertheless, the resulting inferential procedures are known to perform poorly when the dimension of the nuisance parameter is large relative to the sample size and when the information about the parameters is limited. In many such cases, the use of asymptotic normality of analytical modifications of the signed likelihood root is known to recover inferential performance. It is proved here that parametric bootstrap of standard likelihood pivots results in as accurate inferences as analytical modifications of the signed likelihood root do in stratified models with stratum specific nuisance parameters. We focus on the challenging case where the number of strata increases as fast or faster than the stratum samples size. It is also shown that this equivalence holds regardless of whether constrained or unconstrained bootstrap is used. This is in contrast to when the number of strata is fixed or increases slower than the stratum sample size, where we show that constrained bootstrap corrects inference to a higher order than unconstrained bootstrap. Simulation experiments support the theoretical findings and demonstrate the excellent performance of bootstrap in extreme scenarios.
翻译:有关利益标度参数的推论通常取决于普通概率直角点(如经签署的概率根、得分和Wald统计等)的无症状常态性,尽管如此,当扰动参数的尺寸与样本大小相比很大,而且有关参数的信息有限时,由此得出的推论程序就被认为效果不佳。在许多这类情况下,使用对经签署的概率根的分析修改的无症状常性以恢复自推性能。这里证明标准概率直角的准靴子的参数性能是精确的推论,如对经签署的根的分数作分析性修改,在具有分层特定微调参数的分层模型中,其结果就会发生分析性能的改变。我们侧重于一个具有挑战性的案例,即层数的增加速度快于或快于结层样品大小的信息。还表明,无论使用受约束或不受约束的靴杆,这种等同性都保持不变。这与层数的固定或增加速度慢于施压样样样样样样样本大小,我们在此显示,受约束的靴室的极好性实验将显示,其极好的性性性能将显示,比受制的温度的温度的极高。