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Improving the Efficiency of the Nelson–Aalen Estimator: the Naive Local Constant Estimator
Author(s) -
GUILLEN MONTSERRAT,
NIELSEN JENS P.,
PEREZMARIN ANA M.
Publication year - 2007
Publication title -
scandinavian journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.359
H-Index - 65
eISSN - 1467-9469
pISSN - 0303-6898
DOI - 10.1111/j.1467-9469.2006.00541.x
Subject(s) - estimator , mathematics , efficient estimator , minimum variance unbiased estimator , statistics , consistent estimator , stein's unbiased risk estimate , bias of an estimator , variance (accounting) , efficiency , constant (computer programming) , econometrics , computer science , accounting , business , programming language
. The Nelson–Aalen estimator is well known to be an asymptotically efficient estimator of the cumulative hazard function, see Andersen et al. ( Statistical models based on counting processes , Springer‐Verlag, New York, 1993) among many others. In this paper, we show that the efficiency of the Nelson–Aalen estimator can be considerably improved by using more information in the estimation process than the traditional Nelson–Aalen estimator uses. While our approach results in a biased estimator, the variance improvement is substantial. By optimizing the balance between the bias loss and the variance improvement, we obtain results on the efficiency gain. Several examples for known failure time distributions are used to illustrate these ideas.