Abstract
The most popular approach for nonparametric estimation of a regression reliability model, proposed by Beran, is considered in this paper. In this paper, we give the detailed analysis of the selection method for the bandwidth parameter, which is based on minimization of the distance of failure times from kernel estimate of the inverse reliability function. The accuracy of the Beran estimator is studied depending on the plan of experiment (the sample size and the number of values of the explanatory variable) and the way of calculating kernel estimates of the inverse reliability function. We formulate some conclusions on the choice of smoothing parameter and kernel function for the estimates of the inverse reliability function, which give the best accuracy of Beran’s estimator.
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References
Beran, R.: Nonparametic regression with randomly censored survival data. Technical report, Department of Statistics, University of California, Berkeley (1981)
Cox, D.R.: Regression models and life tables (with discussion). J. R. Stat. Soc. Ser. B 34, 187–220 (1972)
Dabrowska, D.M.: Nonparametric quantile regression with censored data. Sankhya: Indian J. Stat. Ser. A 54, 252–259 (1992)
Demin, V.A., Chimitova, E.V.: Choice of optimal smoothing parameter for nonparametric estimation of regression reliability model. Tomsk state university. J. Contr. Comput. Sci. 1(22), 50–59 (2012)
Gonzalez, M.W., Cadarso, S.C.: Asymptotic properties of a generalized Kaplan–Meier estimator with some application. J. Nonparametr. Stat. 4, 65–78 (1994)
Hardle, W.: Applied Nonparametric Regression. Cambridge University Press, Cambridge (1992)
Li, G., Datta, S.: A bootstrap approach to nonparametric regression for right censored data. Technical Report, Department of Statistics, University of Georgia, Athens, 30602 (1999)
McKeague, I.W., Utikal, K.J.: Inference for a nonlinear counting process regression model. Ann. Stat. 18, 1172–1187 (1990)
Van Keilegom, I., Akritas, M.G., Veraverbeke, N.: Estimation of the conditional distribution in regression with censored data: a comparative study. Comput. Stat. Data Anal. 35, 487–500 (2001)
Van Keilegom, I.: Nonparametric estimation of the conditional distribution in regression with censored data. Dissertation, Limburgs Universitair Centrum te verdedigen door (1998)
Acknowledgements
This research has been supported by the Russian Ministry of Education and Science (project 2.541.2014K).
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Demin, V., Chimitova, E. (2014). A Method for Selection of the Optimal Bandwidth Parameter for Beran’s Nonparametric Estimator. In: Melas, V., Mignani, S., Monari, P., Salmaso, L. (eds) Topics in Statistical Simulation. Springer Proceedings in Mathematics & Statistics, vol 114. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-2104-1_13
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DOI: https://doi.org/10.1007/978-1-4939-2104-1_13
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