Free area estimation in a partially observed dynamic germ-grain model
The estimation problem of the expected local fraction of free area function for a partially observed dynamic germ-grain model is presented. Properties of the estimators are proved by martingale and product integral methods. Confidence bounds are provided. Furthermore, an estimator of the hazard rate is obtained by the kernel function method and asymptotic properties of the estimator are proved and used to find confidence intervals. By a simulated illustrative example, the qualitative behavior of the estimators is shown.