zbMATH — the first resource for mathematics

Relative density estimation and local bandwidth selection for censored data. (English) Zbl 1030.62027
This paper is concerned with local bandwidth selection for a kernel-type estimator of the relative density (or grade density) when the samples come from two populations under a right random censorship mechanism. A two-stage smoothed plug-in local bandwidth selector with a beta reference is proposed. This estimation procedure is used to analyze the lifetime density in a two-sample problem related to breast cancer. A simulation study is carried out to examine the practical performance of the bandwidth selector.

62G07 Density estimation
62P10 Applications of statistics to biology and medical sciences; meta analysis
KernSmooth; reldist
PDF BibTeX Cite
Full Text: DOI
[1] Bell, C. B.; Doksum, K. A.: Optimal one-sample distribution-free tests and their two-sample extensions. Ann. math. Statist. 37, 120-132 (1966) · Zbl 0142.15703
[2] Brockmann, M.; Gasser, T.; Herrmann, E.: Locally adaptive bandwidth choice for kernel regression estimators. J. amer. Statist. assoc. 88, 1302-1309 (1993) · Zbl 0792.62028
[3] Cao, R.; Janssen, P.; Veraverbeke, N.: Relative density estimation with censored data. Can. J. Statist. 28, 97-111 (2000) · Zbl 1066.62522
[4] ’cwik, J.; Mielniczuk, J.: Data-dependent bandwidth choice for a grade density kernel estimate. Statist. probab. Lett. 16, 397-405 (1993) · Zbl 0764.62035
[5] Gastwirth, J. L.: The first-median test a two-sided version of the control median test. J. amer. Statist. assoc. 63, 692-706 (1968) · Zbl 0162.21805
[6] Gastwirth, J. L.; Wang, J. -L.: Control percentile test procedures for censored data. J. statist. Planning inf. 18, 267-276 (1988) · Zbl 0641.62031
[7] Gray, R. J.: Flexible methods for analyzing survival data using splines, with applications to breast cancer prognosis. J. amer. Statist. assoc. 87, 942-951 (1992)
[8] Handcock, M. S.; Morris, M.: Relative distribution methods in social sciences.. (1999) · Zbl 0949.91029
[9] Hsieh, F.: The empirical process approach for semiparametric two-sample models with heterogeneous treatment effect. J. roy. Statist. soc., ser. B 57, 735-748 (1995) · Zbl 0827.62031
[10] Hsieh, F.; Turnbull, B. W.: Nonparametric and semiparametric estimation of the receiver operating characteristic curve. Ann. statist. 24, 25-40 (1996) · Zbl 0855.62029
[11] Kaplan, E. L.; Meier, P.: Nonparametric estimation from incomplete observations. J. amer. Statist. assoc. 53, 457-481 (1958) · Zbl 0089.14801
[12] Li, G.; Tiwari, R. C.; Wells, M. T.: Quantile comparison functions in two-sample problems with applications to comparisons of diagnostic markers. J. amer. Statist. assoc. 91, 689-698 (1996) · Zbl 0868.62040
[13] Lo, S. H.; Mack, Y. P.; Wang, J. -L.: Density and hazard rate estimation for censored data via strong representation of the kaplan–meier estimator. Probab. theory rel. Fields 80, 461-473 (1989) · Zbl 0637.62039
[14] Müller, H. G.; Stadtmüller, U.: Variable bandwidth kernel estimators of regression curves. Ann. statist. 15, 182-201 (1987) · Zbl 0634.62032
[15] Scott, D. W.; Factor, L. E.: Monte Carlo study of three data-based nonparametric probability density estimators. J. amer. Statist. assoc. 76, 9-15 (1981) · Zbl 0465.62036
[16] Scott, D. W.; Tapia, R. A.; Thompson, J. R.: Kernel density estimation revisited. Nonlinear anal. Theory meth. Appl. 1, 339-372 (1977) · Zbl 0363.62030
[17] Silverman, B. W.: Density estimation.. (1986) · Zbl 0617.62042
[18] Simonoff, J. S.: Smoothing methods in statistics.. (1996) · Zbl 0859.62035
[19] Stute, W.: The bias of kaplan–meier integrals. Scand. J. Statist. 21, 475-484 (1994) · Zbl 0812.62042
[20] Wand, M. P.; Jones, M. C.: Kernel smoothing.. (1995) · Zbl 0854.62043
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.