TY - JOUR
T1 - A penalized simulated maximum likelihood method to estimate parameters for SDEs with measurement error
AU - Sun, Libo
AU - Lee, Chihoon
AU - Hoeting, Jennifer A.
N1 - Publisher Copyright:
© 2018, Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2019/6/1
Y1 - 2019/6/1
N2 - 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.
AB - 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.
KW - Consistency and asymptotic normality
KW - Measurement error
KW - Penalized simulated maximum likelihood estimation
KW - Stochastic differential equations
UR - http://www.scopus.com/inward/record.url?scp=85055690389&partnerID=8YFLogxK
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U2 - 10.1007/s00180-018-0846-3
DO - 10.1007/s00180-018-0846-3
M3 - Article
AN - SCOPUS:85055690389
SN - 0943-4062
VL - 34
SP - 847
EP - 863
JO - Computational Statistics
JF - Computational Statistics
IS - 2
ER -