We consider the problem of estimating parameters of stochastic differentialequations (SDEs) with discrete-time observations that are either completely orpartially observed. The transition density between two observations isgenerally unknown. We propose an importance sampling approach with an auxiliaryparameter when the transition density is unknown. We embed the auxiliaryimportance sampler in a penalized maximum likelihood framework which producesmore accurate and computationally efficient parameter estimates. Simulationstudies in three different models illustrate promising improvements of the newpenalized simulated maximum likelihood method. The new procedure is designedfor the challenging case when some state variables are unobserved and moreover,observed states are sparse over time, which commonly arises in ecologicalstudies. We apply this new approach to two epidemics of chronic wasting diseasein mule deer.
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