Bootstrap-based statistical inference for linear mixed effects under misspecifications
针对线性混合效应模型在模型假设偏离时的推断问题，提出一种基于半参数随机效应自助法的稳健统计方法，通过理论和模拟验证其一致性及对非对称、长尾分布的鲁棒性，并应用于西班牙加利西亚地区家庭收入置信区间构建。
Linear mixed effects are considered excellent predictors of cluster-level parameters in various domains. However, previous research has demonstrated that their performance is affected by departures from model assumptions. Given the common occurrence of these departures in empirical studies, there is a need for inferential methods that are robust to misspecifications while remaining accessible and appealing to practitioners. Statistical tools have been developed for cluster-wise and simultaneous inference for mixed effects under distributional misspecifications, employing a user-friendly semiparametric random effect bootstrap. The merits and limitations of this approach are discussed in the general context of model misspecification. Theoretical analysis demonstrates the asymptotic consistency of the methods under general regularity conditions. Simulations show that the proposed intervals are robust to departures from modelling assumptions, including asymmetry and long tails in the distributions of errors and random effects, outperforming competitors in terms of empirical coverage probability. Finally, the methodology is applied to construct confidence intervals for household income across counties in the Spanish region of Galicia.