Free area estimation in a partially observed dynamic germ-grain model (Q1394557)

The estimation problem of the expected local fraction of the 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, an estimator of the hazard rate \(\alpha(t)= -dS(1)/(S(t)dt)\) 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.