Robust parametric inference for finite Markov chains

Ghosh, Abhik

doi:10.1007/s11749-021-00771-1

Cited by 3 publications

(2 citation statements)

References 25 publications

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“…In a very recent work, Ghosh (2022) proposed robust parametric inference procedures for the finite Markov chain models with general transition probability structures using the minimum DPD approach. The DPD measure and its use in robust estimation were initially introduced in Basu et al (1998) for IID set-ups, which subsequently becomes very popular due to its several nice properties.…”

Section: Literature Surveymentioning

confidence: 99%

Robust and Efficient Parameter Estimation for Discretely Observed Stochastic Processes

Hore¹,

Ghosh²

2022

Preprint

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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.

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Section: Literature Surveymentioning

confidence: 99%

Robust and Efficient Parameter Estimation for Discretely Observed Stochastic Processes

Hore¹,

Ghosh²

2022

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…In a very recent work, [32] proposed robust parametric inference procedures for the finite Markov chain models with general transition probability structures using the minimum DPD approach. The DPD measure and its use in robust estimation were initially introduced in [33] for IID set-ups, which subsequently becomes very popular due to its several nice properties.…”

Section: Literature Surveymentioning

confidence: 99%

Robust and Efficient Parameter Estimation for Discretely Observed Stochastic Processes

Hore

Ghosh

2022

Preprint

Self Cite

View full text Add to dashboard Cite

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 setups and illustrate their benefits over the usual ML estimator for common examples like Poisson process, drifted Brownian motion and auto-regressive models.

show abstract

Robust and efficient parameter estimation for discretely observed stochastic processes

Hore,

Ghosh

2024

Ann Inst Stat Math

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Robust parametric inference for finite Markov chains

Cited by 3 publications

References 25 publications

Robust and Efficient Parameter Estimation for Discretely Observed Stochastic Processes

Robust and Efficient Parameter Estimation for Discretely Observed Stochastic Processes

Robust and Efficient Parameter Estimation for Discretely Observed Stochastic Processes

Robust and efficient parameter estimation for discretely observed stochastic processes

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