论文标题
对具有混合效应的随机微分方程中渐近推断的综述
A review on asymptotic inference in stochastic differential equations with mixed-effects
论文作者
论文摘要
本文是对具有混合效应的随机微分方程估计的最新贡献的调查。这些模型涉及具有常见漂移和扩散函数的N随机微分方程，但随机参数允许过程之间差异。主要目的是估计n个过程共有的随机效应以及可能的其他固定参数的分布。尽管已经提出了许多算法，但与估计相关的理论方面很少研究。这篇评论文章仅着重于具有混合效应的随机微分方程的理论推断。到目前为止，仅在某些非常特定的混合效应扩散模型中考虑了它，在没有测量误差的情况下观察到了明确的估计器。在此框架内，讨论了几个估计量的渐近性能，即参数或非参数。根据该方法考虑了不同的观察方案，将大量个体与大多数情况下的高频观察相关联。
This paper is a survey of recent contributions on estimation in stochastic differential equations with mixed-effects. These models involve N stochastic differential equations with common drift and diffusion functions but random parameters that allow for differences between processes. The main objective is to estimate the distribution of the random effects and possibly other fixed parameters that are common to the N processes. While many algorithms have been proposed, the theoretical aspects related to estimation have been little studied. This review article focuses only on theoretical inference for stochastic differential equations with mixed-effects. It has so far only been considered in some very specific classes of mixed-effect diffusion models, observed without measurement error, where explicit estimators can be defined. Within this framework, the asymptotic properties of several estimators, either parametric or nonparametric, are discussed. Different schemes of observations are considered according to the approach, associating a large number of individuals with, in most cases, high-frequency observations of the trajectories.
