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Likelihood ratio confidence bands in non-parametric regression with censored data

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Li, G. Van Keilegom, Ingrid [UCL]

Let (X, Y) be a random vector, where Y denotes the variable of interest possibly subject to random right censoring, and X is a covariate. We construct confidence intervals and bands for the conditional survival and quantile function of Y given X using a non-parametric likelihood ratio approach. This approach was introduced by Thomas & Grunkemeier (1975), who estimated confidence intervals of survival probabilities based on right censored data. The method is appealing for several reasons: it always produces intervals inside [0, 1], it does not involve variance estimation, and can produce asymmetric intervals. Asymptotic results for the confidence intervals and bands are obtained, as well as simulation results, in which the performance of the likelihood ratio intervals and bands is compared with that of the normal approximation method. We also propose a bandwidth selection procedure based on the bootstrap and apply the technique on a real data set.

Document type Article de périodique (Journal article) – Article de recherche
Access type Accès restreint
Publication date 2002
Language Anglais
Journal information "Scandinavian Journal of Statistics : theory and applications" - Vol. 29, no. 3, p. 547-562 (2002)
Peer reviewed yes
Publisher Blackwell Publ Ltd (Oxford)
issn 0303-6898
e-issn 1467-9469
Publication status Publié
Affiliation UCL - EUEN/STAT - Institut de statistique
Keywords Beran estimator ; confidence band ; confidence interval ; empirical likelihood ; likelihood ratio ; non-parametric regression ; right censoring
Links
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Bibliographic reference Li, G. ; Van Keilegom, Ingrid. Likelihood ratio confidence bands in non-parametric regression with censored data. In: Scandinavian Journal of Statistics : theory and applications, Vol. 29, no. 3, p. 547-562 (2002)
Permanent URL http://hdl.handle.net/2078.1/41714