Asymptotic properties for the semiparametric regression model with randomly censored data |
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Authors: | Qihua Wang Zhongguo Zheng |
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Institution: | (1) Institute of Applied Mathematics, Chinese Academy of Sciences, 100080 Beijing, China;(2) Department of Probability and Statistics, Peking University, 100871 Beijing, China |
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Abstract: | Suppose that the patients’ survival times.Y, are random variables following the semiparametric regression modelY = Xβ +g(T) + ε, where (X,T) is a radom vector taking values inR×0,1],βis an unknown parameter,g (*) is an unknown smooth regression function andE is the random error with zero mean and variance σ2. It is assumed that (X,T) is independent of E. The estimators
andg
n
(*) of P andg(*) are defined, respectively, when the observations are randomly censored on the right and the censoring distribution is
unknown. Moreover, it is shown that
is asymptotically normal andg
n (*) is weak consistence with rateO
p(n-1/3).
Project supported by China Postdoctoral Science Foundation and the National Natural Science Foundation of China. |
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Keywords: | random censorship semiparametric regression asymptotic normality |
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