|
Sign In to gain access to subscriptions and/or personal tools.
|
Comparison of kernel estimators of conditional distribution function and quantile regression under censoring
Ali Gannoun
Ali Gannoun is CNAM, Mathématiques CEDRIC, France
Jérôme Saracco
Jérôme Saracco is Institut de Mathématiques de Bordeaux, Université Bordeaux 1, France GREThA, Université Montesquieu Bordeaux IV, France Jerome.Saracco{at}math.u-bordeaux1.fr
Keming Yu
Keming Yu is Department of Mathematical Sciences, Brunel University, UK
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.
Key Words: censored data conditional quantile kernel estimator local linear estimator survival analysis
References
- Akritas MG (1994) Nearest neighbor estimation of a bivariate distribution under random censoring . The Annals of Statistics, 22, 1299–327 .[CrossRef]
- Beran R (1981) Nonparametric regression with randomly censored survival data, Technical report, University of California, Berkeley .
- Bowman AW and Wright E (2000) Graphical exploration of covariate effects on survival data through nonparametric quantile curves . Biometrics, 56, 563–70 .[CrossRef][Web of Science][Medline]
[Order article via Infotrieve]
- Cai Z (1998) Kernel density and hazard rate estimation for censored dependent data.
- 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.
- Cai Z and Roussas GG (1998) Kaplan-Meier estimator under association . Journal of Multivariate Analysis, 67, 318–48 .[CrossRef][Web of Science]
- Chaudhuri P (1991) Nonparametric estimates of regression quantiles and their local Bahadur representation . The Annals of Statistics, 2, 760–77 .
- Chernozhukov V and Hong H (2002) Three-step censored quantile regression and extramarital affairs . Journal of the American Statistical Association, 97, 872–82 .[CrossRef][Web of Science]
- Cole TJ and Green PJ (1992) Smoothing reference centile curves: the LMS method and penalized likelihood . Statistics in Medicine, 11, 1305–319 .[Web of Science][Medline]
[Order article via Infotrieve]
- Cox DR (1972) Regression models and life-tables . Journal of the Royal Statistical Society, Series B, 34, 187–220 .
- Dabrowska DM (1989) Uniform consistency of kernel conditional Kaplan-Meier estimate . The Annals of Statistics, 17, 1157–167 .[CrossRef]
- Dabrowska DM (1992a) Nonparametric quantile regression with censored data . Sankhy
, Series A, 54, 252–59 . - Dabrowska DM (1992b) Variable bandwidth conditional Kaplan-Meier estimate . Scandinavian Journal of Statistics, 19, 351–61 .[Web of Science]
- Gannoun A, Girard S, Guinot C and Saracco J (2002) Reference curves based on nonparametric quantile regression . Statistics in Medicine, 21, 3119–135 .[CrossRef][Web of Science][Medline]
[Order article via Infotrieve]
- Gannoun A, Saracco J, Yuan A and Bonney GE (2005) Nonparametric quantile regression with censored data . Scandinavian Journal of Statistics, 32, 527–50 .[CrossRef][Web of Science]
- Honore B, Khan S and Powell JL (2002) Quantile regression under random censoring . Journal of Econometrics, 109, 67–105 .[CrossRef][Web of Science]
- Jones MC, Marron JS and Sheather SJ (1996) Progress in data-based bandwidth selection for kernel density estimation . Computational Statistics, 11, 337–81 .[Web of Science]
- Kaplan E and Meier P (1958) Nonparametric estimation from incomplete observation . Journal of the American Statistical Association, 53, 457–81 .[CrossRef][Web of Science]
- Koenker R and Bassett GS (1978) Regression quantiles . Econometrica, 46, 33–50 .[CrossRef][Web of Science]
- Koenker R, Ng P and Portnoy S (1994) Quantile smoothing splines . Biometrika, 81, 673–80 .[Abstract/Free Full Text]
- Koenker R (2000) Galton, Edgeworth, Frish, and prospects for quantile regression in econometrics . Journal of Econometrics, 95, 347–74 .[CrossRef][Web of Science]
- Kohler M, Máthé K and Pintér M (2002) Prediction from randomly right censored data . Journal of Multivariate Analysis, 80, 73–100 .[CrossRef][Web of Science]
- 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 .[CrossRef][Web of Science][Medline]
[Order article via Infotrieve]
- Lejeune MG and Sarda P (1988) Quantile regression: a nonparametric approach . Computational Statististics and Data Analysis, 6, 229–39 .[CrossRef]
- Leonenko NN and Sakhno LS (2001) On the Kaplan-Meier estimator of long-range dependent sequences . Statistical Inference for Stochastic Processes, 4, 17–40 .[CrossRef]
- 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 .[CrossRef][Web of Science]
- 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 .[CrossRef]
- Li G and Van Keilegom I (2002) Likelihood ratio confidence bands in nonparametric regression with censored data . Scandinavian Journal of Statistics, 29, 547–62 .[CrossRef][Web of Science]
- 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 .[CrossRef]
- Portnoy S (2003) Censored quantile regression . Journal of the American Statistical Association, 98, 1001–12 .[CrossRef][Web of Science]
- Truong YK (2000) Asymptotics for hazard regression. Manuscript available on http://www-bios.sph.unc.edu/~truong/man.html
- 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 .[CrossRef][Web of Science]
- 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 .[CrossRef]
- Van Keilegom I and Akritas MG (1999) Transfer of tail information in censored regression models . The Annals of Statistics, 27, 1745–784 .[CrossRef]
- Yu K and Jones MC (1998) Local linear quantile regression . Journal of the American Statistical Association, 93, 228–38 .[CrossRef][Web of Science]
- Yu K, Lu Z and Stander J (2003) Quantile regression: applications and current research areas . The Statistician, 52, 331–50 .
Statistical Modelling, Vol. 7, No. 4,
329-344 (2007)
DOI: 10.1177/1471082X0700700404

CiteULike Complore Connotea Del.icio.us Digg Reddit Technorati Twitter What's this?
|
|