Statistical inference for high dimensional parameters (HDPs) can be based on their intrinsic correlation; that is, parameters that are close spatially or temporally tend to have more similar values. This is why nonlinear mixed-effects models (NMMs) are commonly (and appropriately) used for models with HDPs. Conversely, in many practical applications of NMM, the random effects (REs) are actually correlated HDPs that should remain constant during repeated sampling for frequentist inference. In both scenarios, the inference should be conditional on REs, instead of marginal inference by integrating out REs. In this paper, we first summarize recent theory of conditional inference for NMM, and then propose a bias-corrected RE predictor and confidence interval (CI). We also extend this methodology to accommodate the case where some REs are not associated with data. Simulation studies indicate that this new approach leads to substantial improvement in the conditional coverage rate of RE CIs, including CIs for smooth functions in generalized additive models, as compared to the existing method based on marginal inference.

翻译：高维参数（HDP）的统计推断可基于其内在相关性——即空间或时间上相近的参数往往具有更相似的数值。这正是非线性混合效应模型（NMM）适用于高维参数建模的常规且合理的原因。然而，在NMM的许多实际应用中，随机效应（RE）实际上是相关的HDP，在频率学派推断的重复抽样过程中应保持恒定。在这两种场景下，推断应以随机效应为条件，而非通过对随机效应积分进行边缘推断。本文首先总结了NMM条件推断的最新理论，随后提出了一种偏差校正的随机效应预测器及置信区间（CI）。我们还将该方法扩展至部分随机效应与数据无关的情形。模拟研究表明，与基于边缘推断的现有方法相比，该新方法显著提升了随机效应置信区间（包括广义可加模型中光滑函数的置信区间）的条件覆盖概率。