Quasi-likelihood inference for SDE with mixed-effects observed at high frequency

We consider statistical inference for a class of dynamic mixed-effect models described by stochastic differential equations whose drift and diffusion coefficients simultaneously depend on fixed- and random-effect parameters. Assuming that each process is observed at high frequency and the number of individuals goes to infinity, we propose a stepwise inference procedure and prove its theoretical properties. The methodology is based on suitable quasi-likelihood functions by profiling the random effect in the diffusion coefficient at the first stage, and then taking the marginal distribution in the drift coefficient in the second stage, resulting in a fully explicit and computationally convenient method.