Counting process approach to time sequential and sequential point estimation with censored data

Abstract

Time sequential and sequential point estimation problems with censored data are studied in the parametric counting process context. In each problem, a sequential procedure, based on maximum likelihood estimate, is proposed and is shown to be asymptotically risk efficient. These and other asymptotic results are derived as consequences of standard results in parametric counting process estimation problem.

Keywords:

• Time-sequential point estimation
• sequential point estimation
• maximum likelihood estimate
• parametric counting process
• random censoring
• asymptotic risk-efficiency