School of Mathematics, Jilin University, Changchun, China.
Department of Mathematics and Statistics, University of Regina, Regina, SK, Canada.
Stat Methods Med Res. 2023 Jun;32(6):1169-1192. doi: 10.1177/09622802231164730. Epub 2023 Mar 28.
Most of the studies for longitudinal quantile regression are based on the correct specification. Nevertheless, one specific model can hardly perform precisely under different conditions and assessing which conditions are (approximately) satisfied to determine the optimal one is rather difficult. In the case of the mixed effect model, the misspecification of the fixed effect part will cause a lack of predicting accuracy of random effects, and affect the efficiency of the cumulative function estimator. On the other hand, limited research has focused on incorporating multiple candidate procedures in longitudinal data analysis, which is of current emergency. This paper proposes an exponential aggregation weighting algorithm for longitudinal quantile regression. Based on the secondary smoothing loss function, we establish oracle inequalities for aggregated estimator. The proposed method is applied to evaluate the cumulative th quantile function for additive mixed effect model with right-censored history process, and an aggregation-based best linear prediction for random effects is constructed as well. We show that the asymptotic properties are conveniently imposed owing to the smoothing scheme. Simulation studies are carried out to exhibit the rationality, and our method is illustrated to analyze the data set from a multicenter automatic defibrillator implantation trial.
大多数纵向分位数回归的研究都是基于正确的规范。然而，一个特定的模型很难在不同的条件下精确地表现，并且评估哪些条件（近似）满足以确定最佳条件是相当困难的。在混合效应模型的情况下，固定效应部分的Specification 错误会导致随机效应预测精度的缺乏，并影响累积函数估计器的效率。另一方面，目前紧急需要的是将多个候选过程纳入纵向数据分析中。本文提出了一种用于纵向分位数回归的指数聚合加权算法。基于二次平滑损失函数，我们为聚合估计量建立了 Oracle 不等式。所提出的方法应用于评估带有右删失历史过程的可加混合效应模型的累积 th 分位数函数，并构建了随机效应的基于聚合的最佳线性预测。我们表明，由于平滑方案，很方便地施加了渐近性质。模拟研究表明了该方法的合理性，并通过分析来自多中心自动除颤器植入试验的数据来举例说明该方法。
