Sequential estimation for semiparametric models with application to the proportional hazards model

摘要: Abstract In this paper, we show that if the Euclidean parameter of a semiparametric model can be estimated through an estimating function, extend straightforwardly conditions by Dmitrienko and Govindarajulu [2000. Ann. Statist. 28 (5), 1472–1501] in order to prove estimator indexed any regular sequence (sequential estimator), has same asymptotic behavior as non-sequential estimator. These also allow us obtain normality stopping rule, for special case sequential confidence sets. results are applied proportional hazards model, which after slight modifications, classical assumptions given Andersen Gill [1982. 10(4), 1100–1120] sufficient version well-known [Cox, 1972. J. Roy. Soc. Ser. B (34), 187–220] partial maximum likelihood To result need establish strong convergence regression estimator, involving mainly exponential inequalities both continuous martingales some basic empirical processes. A typical example fixed-width interval is illustrated Monte Carlo study.