RESEARCH ARTICLE

Weighted local polynomial estimations of a non-parametric function with censoring indicators missing at random and their applications

  • Jiangfeng WANG , 1,2 ,
  • Yangcheng ZHOU 1 ,
  • Ju TANG 1
Expand
  • 1. School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou 310018, China
  • 2. Collaborative Innovation Center of Statistical Data Engineering, Technology & Application, Zhejiang Gongshang University, Hangzhou 310018, China

Published date: 15 Feb 2022

Copyright

2022 Higher Education Press

Abstract

In this paper, we consider the weighted local polynomial calibration estimation and imputation estimation of a non-parametric function when the data are right censored and the censoring indicators are missing at random, and establish the asymptotic normality of these estimators. As their applications, we derive the weighted local linear calibration estimators and imputation estimations of the conditional distribution function, the conditional density function and the conditional quantile function, and investigate the asymptotic normality of these estimators. Finally, the simulation studies are conducted to illustrate the finite sample performance of the estimators.

Cite this article

Jiangfeng WANG , Yangcheng ZHOU , Ju TANG . Weighted local polynomial estimations of a non-parametric function with censoring indicators missing at random and their applications[J]. Frontiers of Mathematics in China, 2022 , 17(1) : 117 -139 . DOI: 10.1007/s11464-022-1005-2

1
Brunel E, Comte F, Guilloux A. Nonparametric estimation for survival data with censoring indicators missing at random. J Statist Plann Inference, 2013, 143 (10): 1653- 1671

DOI

2
Dikta G. On semiparametric random censorship models. J Statist Plann Inference, 1998, 66 (2): 253- 279

DOI

3
El Ghouch A, Van Keilegom I. Non-parametric regression with dependent censored data. Scand J Statist, 2008, 35 (2): 228- 247

DOI

4
Fan J Q. Local linear regression smoothers and their minimax efficiencies. Ann Statist, 1993, 21 (1): 196- 216

5
Fan J Q, Gijbels I. Censored regression: local linear approximations and their applications. J Amer Statist Assoc, 1994, 89 (426): 560- 570

DOI

6
Fan J Q, Yao Q W, Tong H. Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems. Biometrika, 1996, 83 (1): 189- 206

DOI

7
Guessoum Z, Ould-Saïd E. On nonparametric estimation of the regression function under random censorship model. Statist Decisions, 2008, 26 (3): 159- 177

8
Guessoum Z, Ould-Saïd E. Central limit theorem for the kernel estimator of the regression function for censored time series. J Nonparametr Stat, 2012, 24 (2): 379- 397

DOI

9
Li X Y, Wang Q H. The weighted least square based estimators with censoring indicators missing at random. J Statist Plann Inference, 2012, 142 (11): 2913- 2925

DOI

10
Liang H Y, de Uña-Álvarez J. Asymptotic properties of conditional quantile estimator for censored dependent observations. Ann Inst Statist Math, 2011, 63 (2): 267- 289

DOI

11
Little R J A, Rubin D B. Statistical Analysis with Missing Data, Second Edition, Wiley Series in Probability and Statistics, Hoboken, NJ: Wiley-Interscience, 2002

12
McKeague I W, Subramanian S. Product-limit estimators and Cox regression with missing censoring information. Scand J Statist, 1998, 25 (4): 589- 601

DOI

13
Nadaraya E A. On estimating regression. Theory Probab Appl, 1964, 9 (1): 141- 142

DOI

14
Ould-Saïd E. A strong uniform convergence rate of kernel conditional quantile estimator under random censorship. Statist Probab Lett, 2006, 76 (6): 579- 586

DOI

15
Shen Y, Liang H Y. Quantile regression for partially linear varying-coefficient model with censoring indicators missing at random. Comput Statist Data Anal, 2018, 117: 1- 18

DOI

16
Silverman B W. Some aspects of the spline smoothing approach to nonparametric regression curve fitting, with discussion. J Roy Statist Soc Ser B, 1985, 47 (1): 1- 52

17
Tang L J, Zhou Z G, Wu C C. Weighted composite quantile estimation and variable selection method for censored regression model. Statist Probab Lett, 2012, 82 (3): 653- 663

DOI

18
Wang J L, Zheng M. Nonparametric regression estimation with missing censoring indicators. Chinese J Appl Probab Statist, 2014, 30 (5): 476- 490

19
Wang Q H, Ng K W. Asymptotically efficient product-limit estimators with censoring indicators missing at random. Statist Sinica, 2008, 18 (2): 749- 768

20
Yao M, Wang J F, Lin L. Double-kernel local linear estimator of conditional quantile under left-truncated and dependent data. Acta Math Sin (Chin Ser), 2018, 61 (6): 963- 980

21
Yu K M, Jones M C. Local linear quantile regression. J Amer Statist Assoc, 1998, 93 (441): 228- 237

DOI

22
Zhou L Z. A simple censored median regression estimator. Statist Sinica, 2016, 16 (3): 1043- 1058

23
Zhou X, Sun L Q. Additive hazards regression with missing censoring information. Statist Sinica, 2003, 13 (4): 1237- 1257

Outlines

/