论文标题
离散观察到的随机过程的强大而有效的参数估计
Robust and Efficient Parameter Estimation for Discretely Observed Stochastic Processes
论文作者
论文摘要
在各种实际情况下，我们遇到来自随机过程的数据，这些数据可以通过适当的参数模型进行有效建模，以进行后续统计分析。不幸的是，基于最大可能性（ML）原理的最常见估计和推理方法易受与假定模型或数据污染的小偏差，因为它们众所周知缺乏鲁棒性。由于替代性非参数程序通常会失去显着效率，因此在本文中，我们从参数随机过程模型中开发了一个可靠的参数估计程序，用于离散观察到的数据，该过程利用了最小距离推断框架中流行密度幂差异度量的良好性能。特别是，我们在这里定义了独立增量和马尔可夫过程的最小密度差估计器（MDPDE）。我们在这些依赖的随机过程设置中为拟议的MDPDE建立了渐近的一致性和分布结果，并说明了它们比通常ML估计量的益处，例如Poisson过程，如Poisson工艺，漂移的Brownian Motion和自动登记模型。
In various practical situations, we encounter data from stochastic processes which can be efficiently modelled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, the most common estimation and inference methods based on the maximum likelihood (ML) principle are susceptible to minor deviations from assumed model or data contamination due to their well known lack of robustness. Since the alternative non-parametric procedures often lose significant efficiency, in this paper, we develop a robust parameter estimation procedure for discretely observed data from a parametric stochastic process model which exploits the nice properties of the popular density power divergence measure in the framework of minimum distance inference. In particular, here we define the minimum density power divergence estimators (MDPDE) for the independent increment and the Markov processes. We establish the asymptotic consistency and distributional results for the proposed MDPDEs in these dependent stochastic process set-ups and illustrate their benefits over the usual ML estimator for common examples like Poisson process, drifted Brownian motion and auto-regressive models.
