{"title":"Robust and efficient parameter estimation for discretely observed stochastic processes","authors":"Rohan Hore, Abhik Ghosh","doi":"10.1007/s10463-024-00922-9","DOIUrl":null,"url":null,"abstract":"<div><p>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.</p></div>","PeriodicalId":55511,"journal":{"name":"Annals of the Institute of Statistical Mathematics","volume":"77 3","pages":"387 - 424"},"PeriodicalIF":0.8000,"publicationDate":"2024-12-23","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Annals of the Institute of Statistical Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1007/s10463-024-00922-9","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"STATISTICS & PROBABILITY","Score":null,"Total":0}
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.
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.