Abstract
This research proposes the local polynomial smoothing of the Kaplan–Meier estimate under the fixed design setting. This allows the development of estimates of the distribution function (equivalently the survival function) and its derivatives under the random right censoring model. The asymptotic properties of the estimate, including its asymptotic normality are all established herein.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Bagkavos, D., Patil, P.N.: Local polynomial fitting in failure rate estimation. IEEE Transactions on Reliability 56, 126–163 (2008)
Bagkavos, D.: Local linear hazard rate estimation and bandwidth selection. Ann. Inst. Stat. Math. 63, 1019–1046 (2011)
Cheng, M.-Y., Peng, L.: Regression modeling for nonparametric estimation of distribution and quantile functions. Statist. Sinica. 12, 1043–1060 (2002)
Cheng, M.-Y., Fan, J., Marron, J.S.: On automatic boundary corrections. Ann. Statist. 25, 1691–1708 (1997)
Fan, J., Gijbels, I.: Local polynomial modeling and its applications. Chapman and Hall, London (1996)
Jones, M.C., Sheather, S.J.: Using non-stochastic terms to advantage in kernel-based estimation of integrated squared density derivatives. Statistics and Probability Letters 11, 511–514 (1991)
Huang, Z., Maesono, Y.: Edgeworth expansion for kernel estimators of a distribution function. Bulletin of informatics and cybernetics 10, 1–10 (2014)
Hall, P., Sheather, S., Jones, M.C., Marron, J.S.: On optimal data based bandwidth selection in kernel density estimation. Biometrika 78, 521–530 (1991)
Garcia-Soidán, P.H., González-Manteiga, W., Prada-Sánchez, J.M.: Edgeworth expansions for nonparametric distribution estimation with applications. J. Statist. Plann. Inference 65, 213–231 (1997)
Gulati, S., Padgett, W.J.: Families of smooth confidence bands for the survival function under the general random censorship model. Lifetime Data Anal. 2, 349–362 (1996)
Kaplan, E.L., Meier, P.: Nonparametric estimation from incomplete observations. J. Amer. Statist. Assoc. 53, 457–481 (1958)
Karunamuni, R., Yang, S.: Weak and strong uniform consistency rates of kernel density estimates for randomly censored data. Can. J. Statist. 19, 349–359 (1991)
Marron, J.S., Padgett, W.J.: Asymptotically optimal bandwidth selection for kernel density estimators from randomly right censored samples. Ann. Statist. 15, 1520–1535 (1987)
Petrov, V.: Limit Theorems of Probability Theory: sequences of independent random variables. Oxford University Press, New York (1985)
Susarla, V., Tsai, W. Y.and Van Ryzin, J.(1984). A Buckley–James-type estimator for the mean with censored data, Biometrika, 71 624–625
Acknowledgements
The authors deeply thank an anonymous referee for the valuable comments and suggestions provided, leading in significantly improving this article.
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2020 Springer Nature Switzerland AG
About this paper
Cite this paper
Ioannides, D., Bagkavos, D. (2020). Smooth Nonparametric Survival Analysis. In: La Rocca, M., Liseo, B., Salmaso, L. (eds) Nonparametric Statistics. ISNPS 2018. Springer Proceedings in Mathematics & Statistics, vol 339. Springer, Cham. https://doi.org/10.1007/978-3-030-57306-5_22
Download citation
DOI: https://doi.org/10.1007/978-3-030-57306-5_22
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-57305-8
Online ISBN: 978-3-030-57306-5
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)