Browse > Article
http://dx.doi.org/10.4134/JKMS.2007.44.3.525

ASYMPTOTIC NORMALITY OF ESTIMATOR IN NON-PARAMETRIC MODEL UNDER CENSORED SAMPLES  

Niu, Si-Li (DEPARTMENT OF APPLIED MATHEMATICS TONGJI UNIVERSITY)
Li, Qlan-Ru (DEPARTMENT OF APPLIED MATHEMATICS TONGJI UNIVERSITY)
Publication Information
Journal of the Korean Mathematical Society / v.44, no.3, 2007 , pp. 525-539 More about this Journal
Abstract
Consider the regression model $Y_i=g(x_i)+e_i\;for\;i=1,\;2,\;{\ldots},\;n$, where: (1) $x_i$ are fixed design points, (2) $e_i$ are independent random errors with mean zero, (3) g($\cdot$) is unknown regression function defined on [0, 1]. Under $Y_i$ are censored randomly, we discuss the asymptotic normality of the weighted kernel estimators of g when the censored distribution function is known or unknown.
Keywords
censored sample; non-parametric regression model; weighted kernel estimator; asymptotic normality;
Citations & Related Records

Times Cited By Web Of Science : 0  (Related Records In Web of Science)
Times Cited By SCOPUS : 0
연도 인용수 순위
  • Reference
1 B. L. S. Prakasa Rao, Asymptotic theory of statistical inference, Wiley Series in Probability and Mathematical Statistics: Probability and Mathematical Statistics. John Wiley & Sons, Inc., New York, 1987
2 Q. H. Wang, Some convergence properties of weighted kernel estimators of regression functions under random censorship, Acta Math. Appl. Sin. 19 (1996), no. 3, 338-350
3 H. Koul, V. Susarla and J. Van Ryzin, Regression analysis with randomly right-censored data, Ann. Statist. 9 (1981), no. 6, 1276-1288   DOI
4 M. B. Priestley and M. T. Chao, Non-parametric function fitting, J. Roy. Statist. Soc. Ser. B 34 (1972), 385-392
5 A. A. Georgiev, Consistent nonparametric multiple regression: the fixed design case, J. Multivariate Anal. 25 (1988), no. 1, 100-110   DOI
6 G. G. Roussas, Consistent regression estimation with fixed design points under dependence conditions, Statist. Probab. Lett. 8 (1989), no. 1, 41-50   DOI   ScienceOn
7 G. G. Roussas, L. T. Tran, and D. A. Ioannides, Fixed design regression for time series: asymptotic normality, J. Multivariate Anal. 40 (1992), no. 2, 262-291   DOI
8 J. K. Benedetti, On the nonparametric estimation of regression functions, J. Roy. Statist. Soc. Ser. B 39 (1977), no. 2, 248-253
9 Y. Fan, Consistent nonparametric multiple regression for dependent heterogeneous processes: the fixed design case, J. Multivariate Anal. 33 (1990), no. 1, 72-88   DOI
10 A. Foldes and L. Rejto, Strong uniform consistency for nonparametric survival curve estimators from randomly censored data, Ann. Statist. 9 (1981), no. 1, 122-129   DOI
11 L. G. Xue, Strong uniform convergence rates of wavelet estimates of regression function under complete and censored data, Acta Math. Appl. Sin. 25 (2002), no. 3, 430-438
12 A. A. Georgiev and W. Greblicki, Nonparametric function recovering from noisy observations, J. Statist. Plann. Inference 13 (1986), no. 1, 1-14   DOI   ScienceOn
13 E. L. Kaplan and P. Meier, Nonparametric estimation from incomplete observations, J. Amer. Statist. Assoc. 53 (1958), 457-481   DOI
14 L. Tran, G. Roussas, S. Yakowitz, and B. T. Van, Fixed-design regression for linear time series, Ann. Statist. 24 (1996), no. 3, 975-991   DOI