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Original Articles

LIMIT THEOREMS FOR ASYMPTOTICALLY MINIMAX ESTIMATION OF A DISTRIBUTION WITH INCREASING FAILURE RATE UNDER A RANDOM MIXED CENSORSHIP/TRUNCATION MODEL

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Pages 1309-1333 | Published online: 02 Sep 2006

REFERENCES

  • Kiefer , J. and Wolfowitz , J. 1976 . Asymptotically Minimax Estimation of Concave and Convex Distribution Functions . Z. Wahrsch. Verw. Gebiete , 34 : 73 – 85 .
  • Grenander , U. 1956 . On the Theory of Mortality Measurement. Part II . Scand. Aktuarietidskrift J. , 39 : 125 – 153 .
  • Wang , J.L. 1986 . Asymptotically Minimax Estimators for Distributions with Increasing Failure Rate . Ann. Statist. , 14 : 1113 – 1131 .
  • Wang , J.L. 1987 . Estimators of a Distribution Function with Increasing Failure Rate Average . J. Statist. Plann. Inference , 16 : 415 – 427 .
  • Hyde , J. 1977 . Testing Survival Under Right Censoring and Left Truncation . Biometrika , 64 : 225 – 230 .
  • Hyde , J. 1980 . “ Survival Analysis with Incomplete Observations ” . In Biostatistics Casebook 31 – 46 . New York : Wiley Series in Probability and Mathematical Statistics: Applied Probability and Statistics .
  • Barlow , R.E. , Bartholomew , D.J. , Bremner , J.M. and Brunk , H.D. 1972 . Statistical Inference Under Order Restrictions New York : Wiley .
  • Robertson , T. , Wright , F.T. and Dykstra , R.L. 1988 . Order Restricted Statistical Inference New York : Wiley .
  • Dvoretzky , A. , Keifer , J. and Wolfowitz , J. 1956 . Asymptotically Minimax Character of the Sample Distribution Function and of the Classical Multinomial Estimator . Ann. Math. Statist. , 27 : 642 – 699 .
  • Keifer , J. and Wolfowitz , J. 1959 . Asymptotically Minimax Character of the Sample Distribution Function for Vector Chance Variables . Ann. Math. Statist. , 30 : 463 – 489 .
  • Millar , P.W. 1979 . Asymptotic Minimax Theorems for the Sample Distribution Function . Z. Wahrsch. Verw. Gebiete , 48 : 233 – 352 .
  • Marshall , A.W. 1970 . “ Discussion of Barlow and van Zwet's Papers ” . In Nonparametric Techniques in Statistical Inference Edited by: Puri , M.L. 175 – 176 . New York : Cambridge University Press .
  • Padgett , W.J. and Wei , L.J. 1980 . Maximum Likelihood Estimation of a Distribution Function with Increasing Failure Rate Based on Censored Observations . Biometrika , 67 : 470 – 474 .
  • Wellner , J.A. 1982 . Asymptotic Optimality of the Product Limit Estimator . Ann. Statist. , 10 : 595 – 602 .
  • Kaplan , E.L. and Meier , P. 1958 . Nonparametric Estimation from Incomplete Observations . J. Amer. Statist. Assoc. , 53 : 457 – 481 .
  • Huang , J. and Wellner , J.A. 1995 . Estimation of a Monotone Density or Monotone Hazard Under Random Censoring . Scand. J. Statist. , 22 : 3 – 33 .
  • Tsai , W.-Y. 1988 . Estimation of the Survival Function with Increasing Failure Rate Based on Left Truncated and Right Censored Data . Biometrika , 75 : 319 – 324 .
  • Pan , W. and Chappell , R. 1998 . Estimating Survival Curves with Left-Truncated and Interval-Censored Data Under Monotone Hazards . Biometrics , 54 : 1053 – 1060 .
  • Pan , W. , Chappell , R. and Kosorok , M.R. 1998 . On Consistency of the Monotone MLE of Survival for Left Truncated and Interval Censored Data . Statist. Probab. Lett. , 38 : 49 – 57 .
  • Birnbaum , Z.W. , Esary , J.D. and Marshall , A.W. 1966 . Stochastic Characterization of Wearout for Components and Systems . Ann. Math. Statist. , 37 : 816 – 825 .
  • Uzuno[gbar]ullari , Ü. and Wang , J.L. 1992 . A Comparison of Hazard Rate Estimators for Left Truncated and Right Censored Data . Biometrika , 79 : 297 – 310 .
  • Tsai , W.-Y. , Jewell , N.P. and Wang , M.C. 1987 . A Note on the Product Limit Estimator Under Right Censoring and Left Truncation . Biometrika , 74 : 883 – 886 .
  • Stute , W. 1993 . Almost Sure Representations of the Product-Limit Estimator for Truncated Data . Ann. Statist. , 21 : 146 – 156 .
  • Gu , M.G. 1995 . Convergence of Increments for Cumulative Hazard Function in a Mixed Censorship-Truncation Model with Application to Hazard Estimators . Statist. Probab. Lett. , 23 : 135 – 139 .
  • Stute , W. 1994 . U-Statistic Processes: A Martingale Approach . Ann. Probab. , 22 : 1725 – 1744 .
  • Stute , W. 1994 . Strong and Weak Representations of Cumulative Hazard Function and Kaplan–Meier Estimators on Increasing Sets . J. Statist. Plann. Inference , 42 : 315 – 329 .
  • Bai , Z.D. , Rao , C.R. and Zhao , L.C. 1988 . Kernel Estimators of Density Function of Directional Data . J. Multivariate Anal. , 27 : 24 – 39 .
  • Puri , P.S. and Singh , H. 1990 . On Recursive Formulas for Isotonic Regression Useful for Statistical Inference Under Order Restrictions . J. Statist. Plann. Inference , 24 : 1 – 11 .

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