Asymptotic Behavior of the Hazard Rate Kernel Estimator Under Truncated and Censored Data

References

• Arcones , M. A. , Giné , E. ( 1995 ). On the law of the iterated logarithm for canonical U-statistics and processes . Stochastic Proc. Appl. 58 : 217 – 245 .
   Web of Science ®Google Scholar
• Benrabah , O. , Ould-Saïd , E. ( 1998 ). On the law of the logarithm for density and hazard rate estimation from truncated and censored data . Technical Report , Vol. 44 , Univ. du Littoral Côte d'Opale .
   Google Scholar
• Gijbels , I. , Wang , T. J. (1993). Strong representation of the survival function for truncated and censored data with applications. J. Multivariate Anal. 47:210–229.
   Web of Science ®Google Scholar
• Gu , M. G. , Lai , T. L. ( 1990 ). Functional laws of the iterated logarithm for the product-limit estimator of a distribution function under random censorship or truncated data . Ann. Probab. 18 : 160 – 189 .
   Web of Science ®Google Scholar
• Kaplan , E. M. , Meier , P. ( 1958 ). Nonparametric estimation from incomplete observations . J. Amer. Statist. Assoc. 53 : 457 – 481 .
   Web of Science ®Google Scholar
• Lai , T. L. , Ying , Z. ( 1991 ). Estimating a distribution function with truncated and censored data . Ann. Statist. 19 : 417 – 442 .
   Web of Science ®Google Scholar
• Lemdani , M. , Ould-Saïd , E. ( 2001 ). Relative deficiency of the Kaplan–Meier estimator with respect to a smoothed estimator . Mathematical Meth. Statist. 10 : 215 – 231 .
   Google Scholar
• Lynden-Bell , D. ( 1971 ). A method of allowing for known observational selection in small samples applied to 3CR quasars . Monthly Notices Roy. Astronom. Soc. 155 : 95 – 118 .
   Web of Science ®Google Scholar
• Massart , P. ( 1990 ). The tight constant in the Dvoretsky–Kiefer–Wolfowitz inequality . Ann. Probab. 18 : 1269 – 1283 .
   Web of Science ®Google Scholar
• Sanchez-Sellero , C. , Ganzález-Manteiga , W. , Cao , R. ( 1999 ). Bandwidth selection in density estimation with truncated and censored data . Ann. Int. Statist. Math. 51 : 51 – 70 .
   Web of Science ®Google Scholar
• Shorack , G. R. , Wellner , J. A. ( 1986 ). Empirical Processes with Applications to Statistics . New-York : Wiley .
   Google Scholar
• Stute , W. ( 1993 ). Almost sure representations of the product-limit estimator for truncated data . Ann. Statist. 21 : 146 – 156 .
   Web of Science ®Google Scholar
• Sun , L. ( 1997 ). Bandwidth choice for hazard rate estimators from left truncated and right censored data . Statist. Probab. Lett. 36 : 101 – 114 .
   Web of Science ®Google Scholar
• Sun , L. , Zhou , Y. ( 1998 ). Sequential confidence bands for densities under truncated and censored data . Statist. Probab. Lett. 40 : 31 – 41 .
   Web of Science ®Google Scholar
• Tsai , W. Y. , Jewell , N. P. , Wang , M. C. ( 1987 ). A note on the product-limit estimator under right censoring and left truncation . Biometrika 74 : 883 – 886 .
   Web of Science ®Google Scholar
• Uzunog¯ullari , U. , Wang , J. L. ( 1992 ). A comparison of hazard rate estimators for left truncation and right censored data . Biometrika 79 : 293 – 310 .
   Google Scholar
• Wang , Q. H. ( 1999 ). Some bounds for the error of an estimator of the hazard function with censored data . Statist. Probab. Lett. 44 : 319 – 326 .
   Google Scholar
• Woodroofe , M. ( 1985 ). Estimating a distribution function with truncated data . Ann. Statist. 13 : 163 – 177 .
   Web of Science ®Google Scholar
• Zhou , Y. ( 1996 ). A note on the TJW product-limit estimator for truncated and censored data . Statist. Probab. Lett. 26 : 381 – 387 .
   Web of Science ®Google Scholar
• Zhou , Y. , Yip , P. S. F. ( 1999 ). Strong representation of the product-limit estimator for left truncated and right censored data . J. Multivariate Anal. 69 : 261 – 280 .
   Web of Science ®Google Scholar