Free area estimation in a partially observed dynamic germ-grainmodel

[摘要] The estimation problem of the expected local fraction of free area functionSfor a partially observed dynamic germ-grain model is presented. Properties of theestimators are proved by martingale and product integral methods. Confidencebounds are provided. Furthermore, an estimator of the hazard rateα(t)=−dS(t)/(S(t)dt)is obtained by the kernel function method andasymptotic properties of the estimator are proved and used to find confidenceintervals. By a simulated illustrative example, the qualitative behavior of theestimators is shown.

[学科分类] 应用数学