Time-Sequential Point Estimation Through Estimating Equations

Abstract

Time-sequential point estimation is studied in the model of fully parametric censored data and Cox's regression model. Both are investigated in the context of counting processes through estimating equations defined by martingales. The concept of information and a related inequality developed in estimating function theory by Godambe are adapted to these models. These suggest some optimality criteria for choosing stopping times as well as estimators. These lead naturally to some sequential procedures, which are shown to be asymptotically efficient with respect to the above criteria.