Semiparametric inference for the recurrent events process by means of a single-index model

References

• Andersen P, Gill R. Cox's regression model for counting processes: a large sample study. Ann Stat. 1982;10:1100–1120. doi: 10.1214/aos/1176345976
   Web of Science ®Google Scholar
• Sun J, Wei LJ. Regression analysis of panel count data with covariate-dependent observation and censoring times. J R Stat Soc Ser B Stat Methodol. 2000;62:293–302. doi: 10.1111/1467-9868.00232
   Web of Science ®Google Scholar
• Lin DY, Wei LJ, Ying Z. Accelerated failure time models for counting processes. Biometrika. 1998;85:605–618. doi: 10.1093/biomet/85.3.605
   Web of Science ®Google Scholar
• Ghosh D. Accelerated rates regression models for recurrent failure time data. Lifetime Data Anal. 2004;10:247–261. doi: 10.1023/B:LIDA.0000036391.87081.e3
   PubMed Web of Science ®Google Scholar
• Ghosh D, Lin D. Semiparametric analysis of recurrent events in the presence of dependent censoring. Biometrics. 2003;59:877–885. doi: 10.1111/j.0006-341X.2003.00102.x
   PubMed Web of Science ®Google Scholar
• Huang CY, Wang MC. Joint modeling and estimation for recurrent event processes and failure time data. J Am Stat Assoc. 2004;99:1153–1165. doi: 10.1198/016214504000001033
   PubMed Web of Science ®Google Scholar
• Huang CY, Qin J, Wang MC. Semiparametric analysis for recurrent event data with time-dependent covariates and informative censoring. Biometrics. 2010;66:39–49. doi: 10.1111/j.1541-0420.2009.01266.x
   PubMed Web of Science ®Google Scholar
• Ichimura H. Semiparametric least squares (SLS) and weighted SLS estimation of single-index models. J Econ. 1993;58:71–120. doi: 10.1016/0304-4076(93)90114-K
   Web of Science ®Google Scholar
• Härdle W, Hall P, Ichimura H. Optimal smoothing in single-index models. Ann Stat. 1993;21:157–178. doi: 10.1214/aos/1176349020
   Web of Science ®Google Scholar
• Xia Y, Tong H, Li WK, Zhu LX. An adaptive estimation of dimension reduction space. J R Stat Soc Ser B Stat Methodol. 2002;64:363–410. doi: 10.1111/1467-9868.03411
   Web of Science ®Google Scholar
• Bouaziz O, Lopez O. Conditional density estimation in a censored single-index regression model. Bernoulli. 2010;16:514–542. doi: 10.3150/09-BEJ221
   Web of Science ®Google Scholar
• Ghosh D, Lin D. Nonparametric analysis of recurrent events and death. Biometrics. 2000;56:554–562. doi: 10.1111/j.0006-341X.2000.00554.x
   PubMed Web of Science ®Google Scholar
• Dauxois JY, Sencey S. Non-parametric tests for recurrent events under competing risks. Scand J Stat. 2009;36: 649–670. doi: 10.1111/j.1467-9469.2009.00642.x
   Web of Science ®Google Scholar
• Bouaziz O, Comte F, Guilloux A. Nonparametric estimation of the intensity function of a recurrent event process. Stat Sin. 2013;23:635–665.
   Web of Science ®Google Scholar
• Stute W. Consistent estimation under random censorship when covariables are present. J Multivariate Anal. 1993;45:89–103. doi: 10.1006/jmva.1993.1028
   Web of Science ®Google Scholar
• Beran R. Nonparametric regression with randomly censored survival data. Technical report. Berkeley (CA): University of California; 1981.
   Google Scholar
• Dabrowska DM. Nonparametric regression with censored survival time data. Scand J Stat. 1987;14:181–197.
   Web of Science ®Google Scholar
• Leurgans S. Linear models, random censoring and synthetic data. Biometrika. 1987;74:301–309. doi: 10.2307/2336144
   Web of Science ®Google Scholar
• Bowman AW. An alternative method of cross-validation for the smoothing of density estimates. Biometrika. 1984;71:353–360. doi: 10.1093/biomet/71.2.353
   Web of Science ®Google Scholar
• Delecroix M, Hristache M, Patilea V. On semiparametric M-estimation in single-index regression. J Stat Plan Inference. 2006;136:730–769. doi: 10.1016/j.jspi.2004.09.006
   Web of Science ®Google Scholar
• Powell JL, Stock JH, Stoker TM. Semiparametric estimation of index coefficients. Econometrica. 1989;57:1403–1430. doi: 10.2307/1913713
   Web of Science ®Google Scholar
• Delecroix M, Härdle W, Hristache M. Efficient estimation in conditional single-index regression. J Multivariate Anal. 2003;86:213–226. doi: 10.1016/S0047-259X(02)00046-5
   Web of Science ®Google Scholar
• Stute W. The central limit theorem under random censorship. Ann Stat. 1995;23:422–439. doi: 10.1214/aos/1176324528
   Web of Science ®Google Scholar
• Van Keilegom I, Akritas MG. Transfer of tail information in censored regression models. Ann Stat. 1999;27: 1745–1784. doi: 10.1214/aos/1017939150
   Web of Science ®Google Scholar
• Sánchez Sellero C, González Manteiga W, Van Keilegom I. Uniform representation of product-limit integrals with applications. Scand J Stat. 2005;32:563–581. doi: 10.1111/j.1467-9469.2005.00453.x
   Web of Science ®Google Scholar
• Lopez O. Single-index regression models with right-censored responses. J Stat Plan Inference. 2009;139:1082–1097. doi: 10.1016/j.jspi.2008.06.012
   Web of Science ®Google Scholar
• der VaartVan AW, Wellner JA. Weak convergence and empirical processes. Springer Series in Statistics. New York (NY): Springer-Verlag; 1996 [with applications to statistics].
   Google Scholar
• Gijbels I, Veraverbeke N. Almost sure asymptotic representation for a class of functionals of the Kaplan–Meier estimator. Ann Stat. 1991;19:1457–1470. doi: 10.1214/aos/1176348256
   Web of Science ®Google Scholar
• Gill R. Large sample behavior of the product-limit estimator on the whole line. Ann Stat. 1983;11:49–58. doi: 10.1214/aos/1176346055
   Web of Science ®Google Scholar
• Sherman RP. Maximal inequalities for degenerate U-processes with applications to optimization estimators. Ann Stat. 1994;22:439–459. doi: 10.1214/aos/1176325377
   Web of Science ®Google Scholar