Abstract
The behavior of the presmoothed density estimator is studied when different ways to estimate the conditional probability of uncensoring are used. The Nadaraya–Watson, local linear and local logistic approach are compared via simulations with the classical Kaplan–Meier estimator. While the local logistic presmoothing estimator presents the best performance, the relative benefits of the local linear versus the Nadaraya–Watson estimator depend very much on the shape of some underlying functions.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
Cao R, Jácome MA (2004) Presmoothed kernel density estimator for censored data. J Nonparametr Stat 16:289–309
Cao R, Cuevas A, González-Manteiga W (1994) A comparative study of several smoothing methods in density estimation. Comput Stat Data Anal 17:153–176
Cao R, López-de-Ullibarri I, Janssen P, Veraverbeke N (2005) Presmoothed Kaplan–Meier and Nelson–Aalen estimators. J Nonparametr Stat 17:31–56
Cox DR, Snell EJ (1989) Analysis of binary date, 2nd edn. Chapman and Hall, London
Crowley J, Hu M (1977) Covariance analysis of heart transplant survival data. J Am Stat Assoc 72:27–36
De Uña-Álvarez J, Rodríguez-Campos MC (2004) Strong consistency of presmoothed Kaplan–Meier integrals when covariables are present. Statistics 38:483–496
Dikta G (1998) On semiparametric random censorship models. J Stat Plann Inference 66:253–279
Dikta G (2000) The strong law under semiparametric random censorship models. J Stat Plann Inference 83:1–10
Fan J (1992) Design-adaptive nonparametric regression. J Am Stat Assoc 87:998–1004
Fan J (1993) Local linear regression smoothers and their minimax efficiency. Ann Stat 21:196–216
Fan J, Gijbels I (1992) Variable bandwidth and local linear regression smoothers. Ann Stat 20:2008–2036
Fan J, Gijbels I (1996) Local polynomial modelling and its applications. Chapman and Hall, London
Fan J, Farmen M, Gijbels I (1998) Local maximum likelihood estimation and inference. J R Stat Soc B 60:591–608
Hall P, Wolff RCL, Wao Q (1999) Methods for estimating a conditional distribution function. J Am Stat Assoc 94:154–163
Jácome MA, Cao R (2007a) Almost sure asymptotic representation for the presmoothed distribution and density estimators for censored data. Statistics (to appear)
Jácome MA, Cao R (2007b) Bandwidth selection for the presmoothed density estimator with censored data. Submitted, available at http://www.udc.es/dep/mate/Dpto_Matematicas/Investigacion/ ie_publicacion/Jacome_Cao_BSPDE.pdf
Kalbfleisch JD, Prentice RL (1980) The statistical analysis of failure time data. Wiley, New York
Kaplan EL, Meier P (1958) Nonparametric estimation from incomplete observations. J Am Stat Assoc 53:457–481
Koziol JA, Green SB (1976) A Cramer-von Mises statistic for randomly censored data. Biometrika 63:465–481
Miller RG, Halpern J (1982) Regression with censored data. Biometrika 69:521–531
Nadaraya EA (1964) On estimating regression. Theor Probab Appl 10:186–190
Ruppert D, Wand MP (1994) Multivariate weighted least squares regression. Ann Stat 22:1346–1370
Sánchez-Sellero C, González-Manteiga W, Cao R (1999) Bandwidth selection in density estimation with truncated and censored data. Ann Inst Stat Math 51:51–70
Stone M (1975) Cross-validatory choice and assessment of statistical predictions (with discussion). J R Stat Soc Ser B 36:111–147
Watson GS (1964) Smooth regression analysis. Shankya Ser A 26:359–372
Ziegler S (1995) Ein modifizierter Kaplan–Meier Sch ätzer. Diploma dissertation, Mathematisches Institut, Justus-Liebig-Universität Gießen
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Jácome, M.A., Gijbels, I. & Cao, R. Comparison of presmoothing methods in kernel density estimation under censoring. Comput Stat 23, 381–406 (2008). https://doi.org/10.1007/s00180-007-0076-6
Received:
Revised:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00180-007-0076-6