Semiparametric Inference in the Proportional Odds Regression Model

References

• Andersen , P. K. and Gill , R. D. 1982 . “Cox's Regression Model for Counting Processes: A Large Sample Study,” . The Annals of Statistics , 10 : 1100 – 1120 .
   Web of Science ®Google Scholar
• Barlow , W. E. and Prentice , R. L. 1988 . “Residuals for Relative-Risk Regression,” . Biometrika , 75 : 65 – 74 .
   Web of Science ®Google Scholar
• Bennett , S. 1983 . “Analysis of Survival Data by the Proportional Odds Model,” . Statistics in Medicine , 2 : 273 – 277 .
   PubMedGoogle Scholar
• Beran , R. J. 1977 . “Minimum Hellinger Distance Estimates for Parametric Models,” . The Annals of Statistics , 5 : 445 – 463 .
   Web of Science ®Google Scholar
• Beran , R. J. 1982 . “Robust Estimation in Models for Independent Non-Identically Distributed Data,” . The Annals of Statistics , 10 : 415 – 428 .
   Web of Science ®Google Scholar
• Cheng , S. C. , Wei , L. J. and Ying , Z. 1995 . “Analysis of Transformation Models With Censored Data,” . Biometrika , 82 : 835 – 845 .
   Web of Science ®Google Scholar
• Cox , D. R. 1972 . “Regression Models and Life-Tables” . Journal of the Royal Statistical Society , 34 : 187 – 220 . (with discussion), Ser. B
   Google Scholar
• Cox , D. R. 1975 . “Partial Likelihood,” . Biometrika , 62 : 269 – 276 .
   Web of Science ®Google Scholar
• Cuzick , J. 1988 . “Rank Regression,” . The Annals of Statistics , 16 : 1369 – 1389 .
   Web of Science ®Google Scholar
• Dabrowska , D. M. and Doksum , K. A. 1988a . “Estimation and Testing in a Two-Sample Generalized Odds-Rate Model,” . Journal of the American Statistical Association , 83 : 744 – 749 .
   Web of Science ®Google Scholar
• Dabrowska , D. M. and Doksum , K. A. 1988b . “Partial Likelihood in Transformation Models With Censored Data,” . Scandinavian Journal of Statistics , 15 : 1 – 23 .
   Web of Science ®Google Scholar
• Donoho , D. L. and Liu , R. C. 1988a . “The ‘Automatic’ Robustness of Minimum Distance Functionals,” . The Annals of Statistics , 16 : 552 – 586 .
   Web of Science ®Google Scholar
• Donoho , D. L. and Liu , R. C. 1988b . “Pathologies of Some Minimum Distance Estimators,” . The Annals of Statistics , 16 : 587 – 608 .
   Web of Science ®Google Scholar
• Fygensen , M. and Ritov , Y. 1994 . “Monotone Estimating Equations for Censored Data,” . The Annals of Statistics , 22 : 732 – 746 .
   Web of Science ®Google Scholar
• Gill , R. 1980 . Censoring and Stochastic Integrals , Amsterdam : Mathimatische Centrum .
   Google Scholar
• Huber , P. J. 1972 . “Robust Statistics: A Review,” . Annals of Mathematical Statistics , 43 : 1041 – 1067 .
   Google Scholar
• Koul , H. 1992 . Weighted Empiricals and Linear Models , Hayward , CA : IMS .
   Google Scholar
• Koul , H. and Dewet , T. 1983 . “Minimum Distance Estimation in a Linear Regression Model,” . The Annals of Statistics , 11 : 921 – 932 .
   Web of Science ®Google Scholar
• Lai , T. L. and Ying , Z. 1988 . “Stochastic Integrals of Empirical-Type Processes With Applications to Censored Regression,” . Journal of Multivariate Analysis , 27 : 334 – 358 .
   Web of Science ®Google Scholar
• Lin , D. Y. , Wei , L. J. and Ying , Z. 1993 . “Checking the Cox Model With Cumulative Sums of Martingale-Based Residuals,” . Biometrika , 80 : 557 – 572 .
   Web of Science ®Google Scholar
• Millar , P. W. 1983 . The Minimax Principle in Asymptotic Statistical Theory , 75 – 265 . New York : Springer-Verlag . Lecture Notes in Mathematics 976
   Google Scholar
• Murphy , S. A. , Rossini , A. J. and Van der Vaart , A. W. 1996 . “Maximum Likelihood Estimation in the Proportional Odds Model,” . Journal of the American Statistical Association , 92 : 968 – 976 .
   Web of Science ®Google Scholar
• Öztürk , Ö. and Hettmansperger , T. P. 1997 . “Generalized Weighted Cramer–von Mises Distance Estimators,” . Biometrika , 84 : 283 – 294 .
   Web of Science ®Google Scholar
• Parr , W. C. and Schucany , W. R. 1980 . “Minimum Distance and Robust Estimation,” . Journal of the American Statistical Association , 75 : 616 – 624 .
   Web of Science ®Google Scholar
• Peto , R. and Peto , J. 1972 . “Asymptotically Efficient Rank Invariant Test Procedures” . Journal of the Royal Statistical Society , 135 : 185 – 206 . (with discussion)
   Google Scholar
• Pettitt , A. N. 1982 . “Proportional Odds Model for Survival Data and Estimates Using Ranks,” . Applied Statistics , 33 : 169 – 175 .
   Web of Science ®Google Scholar
• Prentice , R. L. 1973 . “Exponential Survivals With Censoring and Explanatory Variables,” . Biometrika , 60 : 279 – 288 .
   Web of Science ®Google Scholar
• Prentice , R. L. 1978 . “Linear Rank Tests With Right-Censored Data,” . Biometrika , 65 : 291 – 298 .
   Web of Science ®Google Scholar
• Prentice , R. L. and Hsu , L. 1997 . “Regression on Hazard Ratios and Cross-Ratios in Multivariate Failure Time Analysis,” . Biometrika , 84 : 349 – 364 .
   Web of Science ®Google Scholar
• Shorack , G. R. and Wellner , J. A. 1986 . Empirical Processes With Applications to Statistics , New York : Wiley .
   Google Scholar
• Tsiatis , A. A. 1990 . “Estimating Regression Parameters Using Linear Rank Tests for Censored Data,” . The Annals of Statistics , 18 : 354 – 372 .
   Web of Science ®Google Scholar
• Wu , C. O. 1995 . “Estimating the Real Parameter in a Two-Sample Proportional Odds Model,” . The Annals of Statistics , 23 : 376 – 395 .
   Web of Science ®Google Scholar
• Yang , S. 1992 . “Some Inequalities About the Kaplan–Meier Estimator,” . The Annals of Statistics , 20 : 535 – 544 .
   Web of Science ®Google Scholar
• Yang , S. 1996 . “Weighted Empiricals and the Product-Limit Estimator in the Multiplicative Hazard and Time Transfer Regression Model,” . Statistics & Probability Letters , 30 : 17 – 24 .
   Web of Science ®Google Scholar
• Yang , S. 1997 . “A Generalization of the Product-Limit Estimator With an Application to Censored Regression,” . The Annals of Statistics , 25 : 1088 – 1108 .
   Web of Science ®Google Scholar