Estimation of the conditional distribution in a conditional Koziol-green model
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We introduce a new estimator for the conditional distribution functions under the proportional hazards model of random censorship. Such estimator generalizes the one proposed by Abdushkurov, Chen and Lin when covariates are present. Asymptotic theory is given for this estimator. First, we established the strong consistency, and also obtain the rate of this convergence. Then, an asymptotic representation for the conditional distribution function estimator leads us to derive its asymptotic normality. The practical performance of the estimation procedure is illustrated on a real data set. Finally, as a further application of the new estimator, some functionals of interest in survival exploratory analysis are brieflys discussed.
Key WordsAsymptotic normality consistency proportional hazard regression right censoring
AMS subject classificationprimary 62G07 secondary 62G20
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- Abdushukurov, A.A. (1984). On some estimates of the distribution function under random censorship. In Conference of Young Scientists. Mathematical Institute of the Academic Sciences, Uzbek SSR, Tashkent. VINITI No. 8756-V (in Russian).Google Scholar
- Aerts, M., P. Janssen and N. Veraverbeke (1994). Asymptotic theory for regression quantile estimators in the heteroscedastic regression model. InAsymptotic Statistics (P. Mandl and M. Husková ed) Physica-Verlag, Heidelberg, 151–161.Google Scholar
- Beran, R. (1981). Nonparametric regression with randomly censored survival data. Technical Report, University of California, Berkeley.Google Scholar
- Cheng, P.E. and G.D. Lin (1984). Maximum likelihood estimation of survival function under the Koziol-Green proportional hazard model. Technical Report B-84-5, Institute of Statistics, Academia Sinica, Taipei, Taiwan.Google Scholar
- De Uña, J., W. González-Manteiga and C. Cadarso-Suarez (1997). Bootstrap selection of the smoothing parameter in density estimation under the Koziol-Green model. In:L 1-Statistical Procedures and Related Topics (Y. Dodge ed.) IMS Lecture Notes Monograph Series, vol. 31, Hayward, California, 385–398.Google Scholar
- Fleming, T.R. and D.P. Harrington (1991).Counting Processes and Survival Analysis. Wiley-Interscience.Google Scholar
- Gasser, T. and H.G. Müller (1984). Estimating regression functions and their derivatives by the kernel method.Scandinavian Journal of Statistics,11, 171–185.Google Scholar
- González-Manteiga, W. and C. Cadarso-Suárcz (1991). Linear regression with randomly right-censored data using prior nonparametric estimation. InNonparametric Functional Estimation and Related Topics (G. Roussas ed.) Kluwer Academic Press, 315–328.Google Scholar