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数学进展 - 2020, Vol. 49(4): 463-480
研究论文
删失指标随机缺失下一类非参数函数的加权局部多项式估计及其应用
Weighted Local Polynomial Estimations of a Non-parametric Function with Censoring Indicators Missing at Random and Their Applications

王江峰*, 周杨程, 唐菊
WANG Jiangfeng, ZHOU Yangcheng, TANG Ju

浙江工商大学统计与数学学院, 杭州, 浙江, 310018
School of Statistics and Mathematics, Zhejiang Gongshang University, Hangzhou, Zhejiang, 310018, P. R. China

收稿日期: 2019-05-08
出版日期: 2020-08-11
2020, Vol. 49(4): 463-480
DOI: 10.11845/sxjz.2019049b


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摘要 本文在右删失数据中删失指标部分随机缺失下, 构造了一类非参数函数的校准加权局部多项式估计以及插值加权局部多项式估计, 并建立了这些估计的渐近正态性; 作为该方法的应用, 导出了条件分布函数、条件密度函数以及条件分位数的加权局部线性双核估计和插值加权局部线性双核估计, 并且得到了这些估计的渐近正态性; 最后, 在有限样本下对这些估计进行了模拟.
关键词 局部多项式估计渐近正态性非参数函数删失指标随机缺失    
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 estimator and imputation estimation 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.
Key wordslocal polynomial estimation    asymptotic normality    non-parametric function    censoring indicator    missing at random
PACS:  O212.7  
基金资助:国家社会科学基金(No. 16BTJ029)和浙江省自然科学基金(No. LY18A010007).
通讯作者: E-mail: * wjf2929@163.com   
[1] Brunel E., Comte F. and Guilloux A., Nonparametric estimation for survival data with censoring indicators missing at random, J. Statist. Plann. Inference, 2013, 143(10): 1653-1671.
[2] Dikta G.,On semiparametric random censorship models, J. Statist. Plann. Inference, 1998, 66(2): 253-279.
[3] El Ghouch, A. and Van Keilegom, I., Non-parametric regression with dependent censored data, Scand. J. Statist., 2008, 35(2): 228-247.
[4] Fan J.Q.,Local linear regression smoothers and their minimax efficiencies, Ann. Statist., 1993, 21(1): 196-216.
[5] Fan, J.Q. and Gijbels, I., Censored regression: local linear approximations and their applications, J. Amer. Statist. Assoc., 1994, 89(426): 560-570.
[6] Fan J.Q., Yao Q.W. and Tong H., Estimation of conditional densities and sensitivity measures in nonlinear dynamical systems, Biometrika, 1996, 83(1): 189-206.
[7] Guessoum, Z. and Ould-Saïd, E., On nonparametric estimation of the regression function under random censorship model, Statist. Decisions, 2008, 26(3): 159-177.
[8] Guessoum, Z. and 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.
[9] Li, X.Y. and Wang, Q.H., The weighted least square based estimators with censoring indicators missing at random, J. Statist. Plann. Inference, 2012, 142(11): 2913-2925.
[10] Liang, H.Y. and de Uña-Álvarez, J., Asymptotic properties of conditional quantile estimator for censored dependent observations, Ann. Inst. Statist. Math., 2011, 63(2): 267-289.
[11] Little R.J.A. and 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. and Subramanian, S., Product-limit estimators and Cox regression with missing censoring information, Scand. J. Statist., 1998, 25(4): 589-601.
[13] Nadaraya E.A.,On estimating regression, Theory Probab. Appl., 1964, 9(1): 141-142.
[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.
[15] Shen, Y. and 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.
[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. and Wu C.C., Weighted composite quantile estimation and variable selection method for censored regression model, Statist. Probab. Lett., 2012, 82(3): 653-663.
[18] Wang, J.L. and Zheng, M., Nonparametric regression estimation with missing censoring indicators, Chinese J. Appl. Probab. Statist., 2014, 30(5): 476-490.
[19] Wang, Q.H. and 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. and 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 (in Chinese).
[21] Yu, K.M. and Jones, M.C., Local linear quantile regression, J. Amer. Statist. Assoc., 1998, 93(441): 228-237.
[22] Zhou L.Z.,A simple censored median regression estimator, Statist. Sinica, 2016, 16(3): 1043-1058.
[23] Zhou, X. and Sun, L.Q., Additive hazards regression with missing censoring information, Statist. Sinica, 2003, 13(4): 1237-1257.
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