Kaplan–Meier estimator and hazard estimator for censored negatively superadditive dependent data

References

• Kaplan EL, Meier P. Nonparametric estimation from incomplete observations. J Amer Statist Assoc. 1958;53:457–481. doi: 10.1080/01621459.1958.10501452
   Web of Science ®Google Scholar
• Stute W, Wang J-L. A strong law under random censorship. Ann Stat. 1993;21:1591–1607. doi: 10.1214/aos/1176349273
   Web of Science ®Google Scholar
• Gill RD. Censoring and stochastic integrals. Mathematical Centre tracts, No. 124. Amsterdam: Mathematisch Centrum; 1980.
   Google Scholar
• Breslow N, Crowley J. A large sample study of the life table and product limit estimates under random censorship. Ann Stat. 1974;2:437–453. doi: 10.1214/aos/1176342705
   Web of Science ®Google Scholar
• Peterson AV. Expressing the Kaplan–Meier estimator as a function of empirical subsurvival functions. J Am Statist Assoc. 1977;72:854–858.
   Web of Science ®Google Scholar
• Gill RD. Large sample behavior of the product limit estimator on the whole line. Ann Stat. 1983;11:49–56. doi: 10.1214/aos/1176346055
   Web of Science ®Google Scholar
• Wang J-G. A note on the uniform consistency of the Kaplan–Meier estimator. Ann Stat. 1987;15:1313–1316. doi: 10.1214/aos/1176350507
   Web of Science ®Google Scholar
• Gu MG, Lai TL. Functional laws of the iterated logarithm for the product-limit estimator of a distribution function under random censorship or truncation. Ann Probab. 1990;18:160–189. doi: 10.1214/aop/1176990943
   Web of Science ®Google Scholar
• Stute W. Convergence of Kaplan–Meier estimator in weighted sup-norms. Stat Probab Lett. 1994;20:219–223. doi: 10.1016/0167-7152(94)90045-0
   Web of Science ®Google Scholar
• Bagai I, Prakasa Rao BLS. Estimation of the survival function for stationary associated processes. Stat Probab Lett. 1991;12:385–391. doi: 10.1016/0167-7152(91)90027-O
   Web of Science ®Google Scholar
• Yu H. A Glivenko–Cantelli lemma and weak convergence for empirical processes of associated sequences. Probab Theory Related Fields. 1993;95:357–370. doi: 10.1007/BF01192169
   Web of Science ®Google Scholar
• Shumway RH, Azari AS, Johnson P. Estimating mean concentrations under transformation for environmental data with detection limits. Technometrics. 1988;31:347–356. doi: 10.1080/00401706.1989.10488557
   Web of Science ®Google Scholar
• Ying Z, Wei LJ. The Kaplan–Meier estimate for dependent failure time observations. J Multivariate Anal. 1994;50:17–29. doi: 10.1006/jmva.1994.1031
   Web of Science ®Google Scholar
• Lecoutre J-P, Ould-Sad E. Convergence of the conditional Kaplan–Meier estimate under strong mixing. J Statist Plann Inference. 1995;44:359–369. doi: 10.1016/0378-3758(94)00084-9
   Web of Science ®Google Scholar
• Liang H-Y, Uña-Álvarez J. A Berry–Esseen type bound in kernel density estimation for strong mixing censored samples. J Multivariate Anal. 2009;100:1219–1231. doi: 10.1016/j.jmva.2008.11.001
   Web of Science ®Google Scholar
• Cai ZW, Roussas GG. Kaplan–Meier estimator under association. J Multivariate Anal. 1998;67:318–348. doi: 10.1006/jmva.1998.1769
   Web of Science ®Google Scholar
• Wu QY, Chen PY. Strong representation results of the Kaplan–Meier estimator for censored negatively associated data. J Inequal Appl. 2013;2013: Aiticle ID 340, 9 pages.
   Google Scholar
• Kemperman JHB. On the FKG-inequalities for measures on a partially ordered space. Nederl Akad Wetensch Proc Ser A. 1977;80:313–331. doi: 10.1016/1385-7258(77)90027-0
   Google Scholar
• Hu TZ. Negatively superadditive dependence of random variables with applications. Chinese J Appl Probab Stat. 2000;16:133–144.
   Google Scholar
• Joag-Dev K, Proschan F. Negative association of random variables with applications. Ann Stat. 1983;11(1):286–295. doi: 10.1214/aos/1176346079
   Web of Science ®Google Scholar
• Sung SH. On the strong convergence for weighted sums of random variables. Statist Pap. 2011;52:447–454. doi: 10.1007/s00362-009-0241-9
   Web of Science ®Google Scholar
• Zarei H, Jabbari H. Complete convergence of weighted sums under negative dependence. Statist Pap. 2011;52:413–418. doi: 10.1007/s00362-009-0238-4
   Web of Science ®Google Scholar
• Wang XJ, Si ZY. Complete consistency of the estimator of nonparametric regression model under ND sequence. Statist Pap. 2015;56:585–596.
   Google Scholar
• Christofides TC, Vaggelatou E. A connection between supermodular ordering and positive/negative association. J Multivariate Anal. 2004;88:138–151. doi: 10.1016/S0047-259X(03)00064-2
   Web of Science ®Google Scholar
• Eghbal N, Amini M, Bozorgnia A. Some maximal inequalities for quadratic forms of negative superadditive dependence random variables. Stat Probab Lett. 2010;80:587–591. doi: 10.1016/j.spl.2009.12.014
   Web of Science ®Google Scholar
• Shen Y, Wang XJ, Yang WZ, Hu SH. Almost sure convergence theorem and strong stability for weighted sums of NSD random variables. Acta Math Sinica. Engl Ser. 2013;29(4):743–756. doi: 10.1007/s10114-012-1723-6
   Web of Science ®Google Scholar
• Wang XJ, Deng X, Zheng LL, Hu SH. Complete convergence for arrays of rowwise negatively superadditive-dependent random variables and its applications. Stat: J Theoret Appl Stat. 2014;48(4):834–850. doi: 10.1080/02331888.2013.800066
   Web of Science ®Google Scholar
• Wang XJ, Shen AT, Chen ZY, Hu SH. Complete convergence for weighted sums of NSD random variables and its application in the EV regression model. TEST. 2015;24:166–184. doi: 10.1007/s11749-014-0402-6
   Web of Science ®Google Scholar
• Wang XJ, Xu C, Hu T-C, Volodin A, Hu SH. On complete convergence for widely orthant-dependent random variables and its applications in nonparametric regression model. TEST. 2014;23:607–629. doi: 10.1007/s11749-014-0365-7
   Web of Science ®Google Scholar
• Wang XJ, Hu SH, Yang WZ, Ling NX. Exponential inequalities and inverse moment for NOD sequence. Stat Probab Lett. 2010;80:452–461. doi: 10.1016/j.spl.2009.11.023
   Web of Science ®Google Scholar
• Yang SC. Consistency of nearest neighbor estimator of density function for negative associated samples. Acta Math Appl Sin. 2003;26(3):385–395.
   Google Scholar