Article (Scientific journals)
Polynomial regression with censored data based on preliminary nonparametric estimation.
Heuchenne, Cédric; Van Keilegom, Ingrid
2007In Annals of the Institute of Statistical Mathematics, 59 (2), p. 273-297
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Keywords :
bootstrap; kernel estimation; least squares estimation; linear regression; nonparametric regression; right censoring; survival analysis; bandwidth
Abstract :
[en] Consider the polynomial regression model Y = (beta)0 + beta(1) X + center dot center dot center dot beta X-p(p) + sigma (X)epsilon, where sigma(2)(X) = Var(Y vertical bar X) is unknown, and epsilon is independent of X and has zero mean. Suppose that Y is subject to random right censoring. A new estimation procedure for the parameters beta(0), center dot center dot center dot, beta (p) is proposed, which extends the classical least squares procedure to censored data. The proposed method is inspired by the method of Buckley and James (1979, Biometrika, 66, 429-436), but is, unlike the latter method, a noniterative procedure due to nonparametric preliminary estimation of the conditional regression function. The asymptotic normality of the estimators is established. Simulations are carried out for both methods and they show that the proposed estimators have usually smaller variance and smaller mean squared error than Buckley-James estimators. The two estimation procedures are also applied to a medical and a astronomical data set.
Disciplines :
Mathematics
Physical, chemical, mathematical & earth Sciences: Multidisciplinary, general & others
Author, co-author :
Heuchenne, Cédric ;  Université de Liège - ULiège > HEC - École de gestion de l'ULiège > Statistique appliquée à la gestion et à l'économie
Van Keilegom, Ingrid
Language :
English
Title :
Polynomial regression with censored data based on preliminary nonparametric estimation.
Publication date :
2007
Journal title :
Annals of the Institute of Statistical Mathematics
ISSN :
0020-3157
eISSN :
1572-9052
Publisher :
Springer Heidelberg, Heidelberg, Germany
Volume :
59
Issue :
2
Pages :
273-297
Peer reviewed :
Peer Reviewed verified by ORBi
Available on ORBi :
since 16 April 2009

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