右删失长度偏差数据分位数差的非参数估计

删除或更新信息，请邮件至freekaoyan#163.com(#换成@)

本站小编 Free考研考试/2021-12-27

右删失长度偏差数据分位数差的非参数估计刘玉涛¹, 潘婧², 周勇³1 中央财经大学统计与数学学院北京 100081;
2 中国银联股份有限公司电子商务与电子支付国家工程实验室上海 201201;
3 统计与数据科学前沿理论及应用教育部重点实验室上海, 华东师范大学统计交叉科学研究院和统计学院上海 200241 Nonparametric Estimation of the Quantile Differences for Right-censored and Length-biased Data Yu Tao LIU¹, Jing PAN², Yong ZHOU³1 School of Statistics and Mathematics, Central University of Finance and Economics, Beijing 100081, P. R. China;
2 Research Institute of Electronic Payment, China Unionpay, Shanghai 201201, P. R. China;
3 Key Laboratory of Advanced Theory and Application in Statistics and Data Science, Ministry of Education Institute of Statistics and Interdisciplinary Sciences and School of Statistics, Faculty of Economics and Management, East China Normal University, Shanghai 200241, P. R. China

摘要
图/表
参考文献
相关文章

全文: PDF(855 KB) HTML (1 KB)
输出: BibTeX | EndNote (RIS)

摘要利用长度偏差数据所特有的辅助信息，对带右删失的长度偏差数据的分位数差提出了一种新的非参数估计.该方法提高了估计的有效性，所得的估计量形式简洁，便于计算.同时，本文用经验过程理论建立了该分位数差估计的相合性及渐近正态性，并给出方差估计的重抽样方法.本文还通过数值模拟考察了该估计量在有限样本下的表现，并将其应用到一个关于老年痴呆的实际数据中.

服务

加入引用管理器

E-mail Alert

RSS

收稿日期: 2018-04-17

MR (2010):	O212
	O212.1

基金资助:国家自然科学重大研究计划重点项目（91546202）；国家自然科学基金委重点项目（71331006）；国家自然科学基金（11401603）；中央高校基本科研业务经费（QL18009）；中央财经大学学科建设经费（CUFESAM201811）

通讯作者:潘婧E-mail: panjing1233@163.com

作者简介: 刘玉涛,E-mail:ytliu@cufe.edu.cn;周勇,E-mail:yzhou@amss.ac.cn

引用本文:

刘玉涛, 潘婧, 周勇. 右删失长度偏差数据分位数差的非参数估计[J]. 数学学报, 2020, 63(2): 105-122. Yu Tao LIU, Jing PAN, Yong ZHOU. Nonparametric Estimation of the Quantile Differences for Right-censored and Length-biased Data. Acta Mathematica Sinica, Chinese Series, 2020, 63(2): 105-122.

链接本文:

http://www.actamath.com/Jwk_sxxb_cn/CN/或 http://www.actamath.com/Jwk_sxxb_cn/CN/Y2020/V63/I2/105

[1] Asgharian M., M'Lan C. E., Wolfson D. B., Length-biased sampling with right censoring, Journal of the American Statistical Association, 2002, 97(457):201-209.
[2] Asgharian M., Wolfson D. B., Asymptotoic behavior of the unconditional NPMLE of the length-biased survivor function from right censored prevalent cohort data, The Annals of Statistics, 2005, 33(5):2109-2131.
[3] Asgharian M., Wolfson D. B., Zhang X., Checking stationarity of the incidence rate using prevalent cohort survival data, Statistics in Medicine, 2006, 25(10):1751-1767.
[4] Chen X. P., Shi J. H., Zhou Y., Monotone rank estimation of transformation models with length-biased and right-censored data, Science in China:Mathematics, 2015, 58(10):1-14.
[5] De Uña-álvarez J., Nonparametric estimation under length-biased sampling and type I censoring:a moment based approach, Annals of the Institute of Statistical Mathematics, 2004, 56(4):667-681.
[6] Efron B., Tibshirani R., Bootstrap methods for standard errors, confidence intervals, and other measures of statistical accuracy, Statistical Science, 1986, 1(1):54-77.
[7] Huang C. Y., Qin J. Nonparametric estimation for length-biased and right-censored data, Biometrika, 2011, 98(1):177-186.
[8] Huang C. Y., Qin J., Composite partial likelihood estimation under length-biased sampling, with application to a prevalent cohort study of dementia, Journal of the American Statistical Association, 2012, 107(499):946-957.
[9] Hyde J., Survival Analysis with Incomplete Observations, In Miller R. G., Jr., Efron B., Brown B. W., Jr., Moses L. E. (Eds.), Biostatistics Casebook, Wiley, New York, 1980:31-46.
[10] Kaplan E. L., Meier P., Nonparametric estimation from incomplete observations, Journal of the American Statistical Association, 1958, 53(282):457-481.
[11] Kopczuk W., Saez E., Song J., Earnings inequality and mobility in the United States:evidence from social security data since 1937, The Quarterly Journal of Economics, 2010, 125(1):91-128.
[12] Kvam P., Length bias in the measurements of carbon nanotubes, Technometrics, 2008, 50(4):462-467.
[13] Li Y., Ma H., Wang D., et al., Analyzing the general biased data by additive risk model, Science China:Mathematics, 2017, 60(4):685-700.
[14] Lin C., Zhou Y., Analyzing right-censored and length-biased data with varying-coefficient transformation model, Journal of Multivariate Analysis, 2014, 130:45-63.
[15] Liu P., Wang Y., Zhou Y., Quantile residual lifetime with right-censored and length-biased data, Annals of the Institute of Statistical Mathematics, 2015, 67(5):999-1028.
[16] Ma H. J., Fan C. Y., Zhou Y., Estimating equation methods for quantile regression with length-biased and right censored data (in Chinese), Science China:Mathematics, 2015, 45(12):1981-2000.
[17] Ning J., Qin J., Shen Y., Buckley-James type estimator with right-censored and length-biased data, Biometrics, 2015, 67(4):1369-1378.
[18] Pakes A., Pollard D., Simulation and the asymptotics of optimization estimators, Econometrica, 1989, 57(5):1027-1057.
[19] Reiss R. D., Approximation Distribution of Order Statistics, Springer-Verlag, New York, 1989.
[20] Shen Y., Ning J., Qin J., Analyzing length-biased data with semiparametric transformation and accelerated failure time models, Journal of the American Statistical Association, 2009, 104(487):1192-1202.
[21] Tsai W. Y., Jewell N. P., Wang M. C., A note on the product-limit estimator under right censoring and left truncation, Biometrika, 1987, 74(4):883-886.
[22] Vardi Y., Multiplicative censoring, renewal processes, deconvolution and decreasing density:nonparametric estimation, Biometrika, 1989, 76(4):751-761.
[23] Veraverbeke N., Estimation of the quantiles of the duration of old age, Journal of Statistical Planning and Inference, 2001, 98(1-2):101-106.
[24] Wang M., Nonparametric estimation from cross-sectional survival data, Journal of the American Statistical Association, 1991, 86(413):130-143.
[25] Wang Y., Liu P., Zhou Y., Quantile residual lifetime for left-truncated and right-censored data, Science China:Mathematics, 2015, 58(6):1217-1234.
[26] Wang Y., Zhou Z., Zhou X., et al., Nonparametric and semiparametric estimation of quantile residual lifetime for length-biased and right-censored data, The Canadian Journal of Statistics, 2017, 45(2):220-250.
[27] Xun L., Shao L., Zhou Y., Efficiency of estimators for quantile differences with left truncated and right censored data, Statistics and Probability Letters, 2017, 121:29-36.
[28] Xun L., Zhou Y., Estimators and their asymptotic properties for quantile difference with left truncated and right censored data, Acta Math. Sin., Chin. Ser., 2017, 60(3):451-464.
[29] Zelen M., Forward and backward recurrence times and length biased sampling:Age specific models, Lifetime Data Analysis, 2005, 10(4):325-334.
[30] Zeng D., Lin D. Y., Efficient resampling methods for nonsmooth estimating function, Biostatistics, 2008, 9(2):355-363.
[31] Zhou W., Jing B., Smoothed empirical likelihood confidence intervals for the difference of quantiles, Statistica Sinica, 2003, 13(1):83-95.

[1]	厉诚博, 胡淑兰, 周勇. 长度偏差右删失数据下[1mm]比例均值剩余寿命模型的估计方法[J]. 数学学报, 2018, 61(5): 865-880.
[2]	舒鑫鑫, 张莉, 周勇. 随机缺失数据下样本分位数估计[J]. 数学学报, 2017, 60(5): 865-882.
[3]	荀立, 周勇. 左截断右删失数据分位差估计及其渐近性质[J]. 数学学报, 2017, 60(3): 451-464.
[4]	孙六全;周勇. 左截断右删失下乘积限过程的振动模的强极限定理[J]. Acta Mathematica Sinica, English Series, 1998, 41(5): -.
[5]	周勇. 两种相依样本经验过程增量的收敛速度及其在光滑估计中的应用[J]. Acta Mathematica Sinica, English Series, 1997, 40(4): -.
[6]	陈夏. B-值随机元及经验过程的 Kolmogorov 重对数律[J]. Acta Mathematica Sinica, English Series, 1993, 36(5): 600-619.
[7]	洪圣岩. 截尾情形下随机窗宽核密度估计[J]. Acta Mathematica Sinica, English Series, 1992, 35(5): 710-718.
[8]	张健;成平. PP Kolmogorov-Smirnov统计量其分布尾部的大样本上界[J]. Acta Mathematica Sinica, English Series, 1991, 34(3): 388-402.
[9]	施锡铨. Hodges-Lehmann位置估计的bootstrap逼近[J]. Acta Mathematica Sinica, English Series, 1987, 30(6): 721-728.

PDF全文下载地址:

http://www.actamath.com/Jwk_sxxb_cn/CN/article/downloadArticleFile.do?attachType=PDF&id=23571