Parameter Estimation of Linear Stochastic Differential Equations with Sparse Observations

Abstract

We consider parameter estimation for linear stochastic differential equations with independent experiments observed at infrequent and irregularly spaced follow-up times. The maximum likelihood method is used to obtain an asymptotically consistent estimator. A kernel-weighted score function is proposed for the parameter in drift terms. The strong consistency and the rate of convergence of the estimator are obtained. The numerical results show that the proposed estimator performs well with moderate sample sizes.

Keywords

• kernel-weighted estimation
• linear stochastic differential equations
• geometric Brownian motion
• likelihood function