We considera regression model in which the variable of interest is censored. We
present various nonparametric estimators of the conditional distribution function
and of conditional quantiles. In a simulation study, we compare the performance of
these estimators. Moreover, the local linear estimator of conditional quantile is
applied on a dataset dealing with the effect of age on survival time of kidney
transplant patients.
Akritas MG
(1994)
Nearest neighbor estimation of a bivariate distribution under random censoring
. The Annals of Statistics, 22,
1299–327
.
2.
Beran R
(1981) Nonparametric regression with
randomly censored survival data, Technical report,
University of California, Berkeley
.
3.
Bowman AW
and
Wright E
(2000)
Graphical exploration of covariate effects on survival data through
nonparametric quantile curves
. Biometrics, 56,
563–70
.
4.
Cai Z
(1998) Kernel density and hazard rate
estimation for censored dependent data.
5.
Cai Z
(2003) Weighted local linear approach to
censored nonparametric regression. In
Akritas MG
and
Politis DM
eds, Recent advances and trends in nonparametric statistics.
Elsevier
, 217–31.
6.
Cai Z
and
Roussas GG
(1998)
Kaplan-Meier estimator under association
. Journal of Multivariate Analysis, 67,
318–48
.
7.
Chaudhuri P
(1991)
Nonparametric estimates of regression quantiles and their local Bahadur representation
. The Annals of Statistics, 2,
760–77
.
8.
Chernozhukov V
and
Hong H
(2002)
Three-step censored quantile regression and extramarital affairs
. Journal of the American Statistical Association,
97,
872–82
.
9.
Cole TJ
and
Green PJ
(1992)
Smoothing reference centile curves: the LMS method and penalized likelihood
. Statistics in Medicine, 11,
1305–319
.
10.
Cox DR
(1972)
Regression models and life-tables
. Journal of the Royal Statistical Society, Series B,
34,
187–220
.
11.
Dabrowska DM
(1989)
Uniform consistency of kernel conditional Kaplan-Meier estimate
. The Annals of Statistics, 17,
1157–167
.
12.
Dabrowska DM
(1992a)
Nonparametric quantile regression with censored data
. Sankhyā, Series A, 54,
252–59
.
Gannoun A
,
Girard S
,
Guinot C
and
Saracco J
(2002)
Reference curves based on nonparametric quantile regression
. Statistics in Medicine, 21,
3119–135
.
15.
Gannoun A
,
Saracco J
,
Yuan A
and
Bonney GE
(2005)
Nonparametric quantile regression with censored data
. Scandinavian Journal of Statistics, 32,
527–50
.
16.
Honore B
,
Khan S
and
Powell JL
(2002)
Quantile regression under random censoring
. Journal of Econometrics, 109,
67–105
.
17.
Jones MC
,
Marron JS
and
Sheather SJ
(1996)
Progress in data-based bandwidth selection for kernel density estimation
. Computational Statistics, 11,
337–81
.
18.
Kaplan E
and
Meier P
(1958)
Nonparametric estimation from incomplete observation
. Journal of the American Statistical Association,
53,
457–81
.
19.
Koenker R
and
Bassett GS
(1978)
Regression quantiles
. Econometrica, 46,
33–50
.
20.
Koenker R
,
Ng P
and
Portnoy S
(1994)
Quantile smoothing splines
. Biometrika, 81,
673–80
.
21.
Koenker R
(2000)
Galton, Edgeworth, Frish, and prospects for quantile regression in econometrics
. Journal of Econometrics, 95,
347–74
.
22.
Kohler M
,
Máthé K
and
Pintér M
(2002)
Prediction from randomly right censored data
. Journal of Multivariate Analysis, 80,
73–100
.
23.
Leconte E
,
Poiraud-Casanova S
and
Thomas-Agnan C
(2002)
Smooth conditional distribution function and quantiles under random censorship
. Lifetime Data Analysis, 8,
229–46
.
24.
Lejeune MG
and
Sarda P
(1988)
Quantile regression: a nonparametric approach
. Computational Statististics and Data Analysis, 6,
229–39
.
25.
Leonenko NN
and
Sakhno LS
(2001)
On the Kaplan-Meier estimator of long-range dependent sequences
. Statistical Inference for Stochastic Processes, 4,
17–40
.
26.
Li G
and
Datta D
(2001)
A bootstrap approach to nonparametric regression for right censored data
. Annals of the Institute of Statistical Mathematics,
53,
708–29
.
27.
Li G
and
Doss H
(1995)
An approach to nonparametric regression for life history data using local
linear fitting
. The Annals of Statistics, 23,
787–823
.
28.
Li G
and
Van Keilegom I
(2002)
Likelihood ratio confidence bands in nonparametric regression with censored data
. Scandinavian Journal of Statistics, 29,
547–62
.
29.
McKeague IW
,
Nikabadze AM
and
Sun Y
(1995)
An omnibus test for independence of a survival time from a covariate
. The Annals of Statistics, 23,
450–75
.
30.
Portnoy S
(2003)
Censored quantile regression
. Journal of the American Statistical Association,
98,
1001–12
.
31.
Truong YK
(2000) Asymptotics for hazard
regression. Manuscript available on http://www-bios.sph.unc.edu/~truong/man.html
32.
Van Keilegom I
and
Veraverbeke N
(1998)
Bootstrapping quantiles in a fixed design regression model with censored data
. Journal of Statistical Planning and Inference, 69,
115–31
.
33.
Van Keilegom I
,
Akritas MG
and
Veraverbeke N
(2001)
Estimation of the conditional distribution in regression with censored
data: a comparative study
. Computational Statististics and Data Analysis, 35,
487–500
.
34.
Van Keilegom I
and
Akritas MG
(1999)
Transfer of tail information in censored regression models
. The Annals of Statistics, 27,
1745–784
.
35.
Yu K
and
Jones MC
(1998)
Local linear quantile regression
. Journal of the American Statistical Association,
93,
228–38
.
36.
Yu K
,
Lu Z
and
Stander J
(2003)
Quantile regression: applications and current research areas
. The Statistician, 52,
331–50
.
