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

TL;DR

This paper introduces a new quasi-likelihood inference method for high-frequency observed stochastic differential equation models with mixed effects, allowing efficient estimation of fixed and random effects as the number of subjects increases.

Contribution

It proposes a novel stepwise inference procedure for SDE mixed-effect models, with theoretical validation and explicit computation advantages.

Findings

Method is computationally convenient and explicit.

Theoretical properties are rigorously established.

Effective for high-frequency data with many individuals.

Abstract

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.