标题： 半参数非线性混合效应模型估计的套索型估计量 显示英文标题

标题： Lasso-type estimators for Semiparametric Nonlinear Mixed-Effects Models Estimation

摘要： 非线性混合效应模型（NLMEs）由于近年来在计算方面的进展，在生物计量学研究中得到了广泛应用，特别是在药代动力学研究和HIV动态模型中。然而，这类模型可能对于复杂的纵向数据分析不够灵活。Ke 和 Wang（2001）提出了半参数NLMEs（SNMMs），这些模型在参数和非参数模型的优点之间取得了良好的平衡，比标准的参数NLMEs更加灵活。然而，SNMMs是一种复杂的模型，其估计仍是一个挑战。Ke 和 Wang（2001）提出的估计程序基于参数估计的对数似然近似方法与非参数估计的平滑样条技术的结合。在这项工作中，我们提出了SNMMs中的新估计策略。一方面，我们使用EM算法的随机逼近版本（Delyon 等人，1999）来获得固定效应和方差分量的确切最大似然（ML）和受限最大似然（REML）估计。另一方面，我们提出了一种LASSO型方法来估计未知的非线性函数。我们为此非参数估计量推导出oracle不等式。我们将这两种方法结合在一个通用的估计程序中，并用模拟数据和真实数据进行说明。 显示英文摘要

摘要： Parametric nonlinear mixed effects models (NLMEs) are now widely used in biometrical studies, especially in pharmacokinetics research and HIV dynamics models, due to, among other aspects, the computational advances achieved during the last years. However, this kind of models may not be flexible enough for complex longitudinal data analysis. Semiparametric NLMEs (SNMMs) have been proposed by Ke and Wang (2001). These models are a good compromise and retain nice features of both parametric and nonparametric models resulting in more flexible models than standard parametric NLMEs. However, SNMMs are complex models for which estimation still remains a challenge. The estimation procedure proposed by Ke and Wang (2001) is based on a combination of log-likelihood approximation methods for parametric estimation and smoothing splines techniques for nonparametric estimation. In this work, we propose new estimation strategies in SNMMs. On the one hand, we use the Stochastic Approximation version of EM algorithm (Delyon et al., 1999) to obtain exact ML and REML estimates of the fixed effects and variance components. On the other hand, we propose a LASSO-type method to estimate the unknown nonlinear function. We derive oracle inequalities for this nonparametric estimator. We combine the two approaches in a general estimation procedure that we illustrate with simulated and real data.