Relative density estimation and local bandwidth selection for censored data

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.

[1]  Winfried Stute,et al.  The Bias of Kaplan-Meier Integrals , 1994 .

[2]  B. Turnbull,et al.  NONPARAMETRIC AND SEMIPARAMETRIC ESTIMATION OF THE RECEIVER OPERATING CHARACTERISTIC CURVE , 1996 .

[3]  Joseph L. Gastwirth,et al.  The First-Median Test: A Two-Sided Version of the Control Median Test , 1968 .

[4]  H. Müller,et al.  Variable Bandwidth Kernel Estimators of Regression Curves , 1987 .

[5]  Joseph L. Gastwirth,et al.  CONTROL PERCENTILE TEST PROCEDURES FOR CENSORED DATA , 1988 .

[6]  F. Hsieh.  The Empirical Process Approach for Semiparametric Two‐Sample Models with Heterogeneous Treatment Effect , 1995 .

[7]  Robert Gray,et al.  Flexible Methods for Analyzing Survival Data Using Splines, with Applications to Breast Cancer Prognosis , 1992 .

[8]  Noël Veraverbeke,et al.  Relative Density Estimation with Censored Data , 2000 .

[9]  D. W. Scott,et al.  Kernel density estimation revisited , 1977 .

[10]  David W. Scott,et al.  Monte Carlo Study of Three Data-Based Nonparametric Probability Density Estimators , 1981 .

[11]  M. Handcock,et al.  Relative Distribution Methods in the Social Sciences , 1999 .

[12]  Jane-Ling Wang,et al.  Density and hazard rate estimation for censored data via strong representation of the Kaplan-Meier estimator , 1985 .

[13]  Jan Mielniczuk,et al.  Data-dependent bandwidth choice for a grade density kernel estimate , 1993 .

[14]  J. Simonoff.  Smoothing Methods in Statistics , 1998 .

[15]  T. Gasser,et al.  Locally Adaptive Bandwidth Choice for Kernel Regression Estimators , 1993 .

[16]  M. Wells,et al.  Quantile Comparison Functions in Two-Sample Problems, with Application to Comparisons of Diagnostic Markers , 1996 .

[17]  E. Kaplan,et al.  Nonparametric Estimation from Incomplete Observations , 1958 .

[18]  C. B. Bell,et al.  "Optimal" One-Sample Distribution-Free Tests and Their Two-Sample Extensions , 1966 .