Free area estimation in a partially observed dynamic germ-grain model

The estimation problem of the expected local fraction of free area function S 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, a estimator of the hazard rate α(t) = − dS(t)/(S(t)dt) 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.