Robust and efficient parameter estimation for discretely observed stochastic processes

IF 0.8 4区 数学 Q3 STATISTICS & PROBABILITY
Rohan Hore, Abhik Ghosh
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引用次数: 0

Abstract

In various practical situations, we encounter data from stochastic processes which can be efficiently modeled by an appropriate parametric model for subsequent statistical analyses. Unfortunately, maximum likelihood (ML) estimation, the most common approach, is sensitive to slight model deviations or data contamination due to its well-known lack of robustness. Since the non-parametric alternatives often sacrifice 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 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 setups and illustrate their benefits over the usual ML estimator for common examples like the Poisson process, drifted Brownian motion and the auto-regressive models.

离散观测随机过程的鲁棒有效参数估计
在各种实际情况下,我们会遇到随机过程的数据,这些数据可以通过适当的参数模型有效地建模,以便后续的统计分析。不幸的是,最大似然(ML)估计是最常见的方法,由于众所周知的缺乏鲁棒性,它对轻微的模型偏差或数据污染很敏感。由于非参数替代方案往往牺牲效率,在本文中,我们开发了一种鲁棒的参数估计程序,该程序利用了流行的密度功率散度度量的良好性质,用于参数随机过程模型的离散观测数据。特别地,我们定义了独立增量和马尔可夫过程的最小密度功率发散估计量(MDPDE)。我们在这些相关随机过程设置中建立了所提出的mdpde的渐近一致性和分布结果,并说明了它们相对于泊松过程、漂移布朗运动和自回归模型等常见示例的通常ML估计器的优点。
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来源期刊
CiteScore
2.00
自引率
0.00%
发文量
39
审稿时长
6-12 weeks
期刊介绍: Annals of the Institute of Statistical Mathematics (AISM) aims to provide a forum for open communication among statisticians, and to contribute to the advancement of statistics as a science to enable humans to handle information in order to cope with uncertainties. It publishes high-quality papers that shed new light on the theoretical, computational and/or methodological aspects of statistical science. Emphasis is placed on (a) development of new methodologies motivated by real data, (b) development of unifying theories, and (c) analysis and improvement of existing methodologies and theories.
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