A penalized simulated maximum likelihood method to estimate parameters for SDEs with measurement error

Libo Sun, Chihoon Lee, Jennifer A. Hoeting

Research output: Contribution to journalArticle

Abstract

The penalized simulated maximum likelihood (PSML) approach can be used to estimate parameters for a stochastic differential equation model based on completely or partially observed discrete-time observations. The PSML uses an auxiliary variable importance sampler and parameters are estimated in a penalized maximum likelihood framework. In this paper, we extend the PSML to allow for measurement error, including unknown initial conditions. Simulation studies for two stochastic models and a real world example aimed at understanding the dynamics of chronic wasting disease illustrate that our method has favorable performance in the presence of measurement error. PSML reduces both the bias and root mean squared error as compared to existing methods. Lastly, we establish consistency and asymptotic normality for the proposed estimators.

Original languageEnglish (US)
Pages (from-to)847-863
Number of pages17
JournalComputational Statistics
Volume34
Issue number2
DOIs
StatePublished - Jun 1 2019

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Simulated Maximum Likelihood
Penalized Maximum Likelihood
Maximum Likelihood Method
Measurement errors
Measurement Error
Maximum likelihood
Estimate
Discrete Time Observations
Chronic Disease
Auxiliary Variables
Stochastic models
Asymptotic Normality
Mean Squared Error
Stochastic Equations
Stochastic Model
Initial conditions
Differential equations
Simulated maximum likelihood
Stochastic differential equations
Measurement error

All Science Journal Classification (ASJC) codes

  • Computational Mathematics
  • Statistics and Probability
  • Statistics, Probability and Uncertainty

Cite this

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A penalized simulated maximum likelihood method to estimate parameters for SDEs with measurement error. / Sun, Libo; Lee, Chihoon; Hoeting, Jennifer A.

In: Computational Statistics, Vol. 34, No. 2, 01.06.2019, p. 847-863.

Research output: Contribution to journalArticle

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