A penalized simulated maximum likelihood approach in parameter estimation for stochastic differential equations. (English) Zbl 1507.62162
Summary: We consider the problem of estimating parameters of stochastic differential equations (SDEs) with discrete-time observations that are either completely or partially observed. The transition density between two observations is generally unknown. We propose an importance sampling approach with an auxiliary parameter when the transition density is unknown. We embed the auxiliary importance sampler in a penalized maximum likelihood framework which produces more accurate and computationally efficient parameter estimates. Simulation studies in three different models illustrate promising improvements of the new penalized simulated maximum likelihood method. The new procedure is designed for the challenging case when some state variables are unobserved and moreover, observed states are sparse over time, which commonly arises in ecological studies. We apply this new approach to two epidemics of chronic wasting disease in mule deer.
MSC:
| 62-08 | Computational methods for problems pertaining to statistics |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
| 62M05 | Markov processes: estimation; hidden Markov models |
| 62P10 | Applications of statistics to biology and medical sciences; meta analysis |
Keywords:
chronic wasting disease; Euler-Maruyama scheme; penalized simulated maximum likelihood estimation; partially observed discrete sparse data; auxiliary importance sampling; stochastic differential equationsReferences:
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