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Miscellany

Nelson–Aalen and product-limit estimation in selection bias models for censored populations

Pages 761-777 | Received 01 May 2003, Accepted 01 Dec 2003, Published online: 31 Jan 2007

References

References

  • Asgharian , M , M'Lan , CE and Wolfson , DB . (2002) . Length-biased sampling with right-censoring: an unconditional approach . Journal of the American Statistical Association , 97 : 201 – 209 .
  • Cheng , PE and Lin , GD . (1987) . Maximum likelihood estimation of a survival function under the Koziol–Green proportional hazards model . Statistics & Probability Letters , 5 : 75 – 80 .
  • Cristóbal , JA and Alcalá , JT . (2000) . Nonparametric regression estimators for length biased data . Journal of Statistical Planning and Inference , 89 : 145 – 168 .
  • Gilbert , PB . (2000) . Large sample theory of maximum likelihood estimates in semiparametric biased sampling models . The Annals of Statistics , 28 : 151 – 194 .
  • Gilbert , PB , Lele , SR and Vardi , Y . (1999) . Maximum likelihood estimation in semiparametric selection bias models with applications to AIDS vaccine trials . Biometrika , 86 : 27 – 43 .
  • Gill , RD , Vardi , Y and Wellner , JA . (1988) . Large sample theory of empirical distributions in biased sampling models . The Annals of Statistics , 16 : 1069 – 1112 .
  • Kaplan , E and Meier , P . (1958) . Nonparametric estimation from incomplete observations . Journal of the American Statistical Association , 53 : 457 – 481 .
  • Lai , TL and Ying , Z . (1991) . Estimating a distribution function with truncated and censored data . The Annals of Statistics , 19 : 417 – 442 .
  • de la Peña VH Giné E (1999) Decoupling from Dependence to Independence, Springer New York
  • Serfling RJ (1980) Approximation Theorems of Mathematical Statistics, Wiley New York
  • Stute , W . (1993) . Almost sure representations of the product-limit estimator for truncated data . The Annals of Statistics , 21 : 146 – 156 .
  • Tsai , WY , Jewell , NP and Wang , MC . (1987) . A note on the product-limit estimator under right censoring and left truncation . Biometrika , 74 : 883 – 886 .
  • de Uña-Álvarez , J . (2000) . Strong consistency of the jackknife estimate of variance and covariance for Koziol–Green integrals . Statistics , 34 : 301 – 352 .
  • de Uña-Álvarez , J . (2002) . Product-limit estimation for length-biased censored data . Test , 11 : 109 – 126 .
  • Vardi , Y . (1982) . Nonparametric estimation in the presence of length bias . The Annals of Statistics , 10 : 616 – 620 .
  • Vardi , Y . (1985) . Empirical distributions in selection bias models (with discussion) . The Annals of Statistics , 13 : 178 – 205 .
  • Wang , M-C . (1991) . Nonparametric estimation from cross-sectional survival data . Journal of the American Statistical Association , 86 : 130 – 143 .
  • Winter , BB and Földes , A . (1988) . A product-limit estimator for use with length-biased data . Canadian Journal of Statistics , 16 : 337 – 355 .
  • Wu , CO . (2000) . Local polynomial regression with selection biased data . Statistica Sinica , 10 : 789 – 817 .
  • Zhou , Y . (1996) . A note on the TJW product-limit estimator for truncated and censored data . Statistics & Probability Letters , 26 : 381 – 387 .
  • Zhou , Y and Yip , PSF . (1999) . A strong representation of the product-limit estimator for left truncated and right censored data . Journal of Multivariate Analysis , 69 : 261 – 280 .

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