Variable Bandwidths for Nonparametric Hazard Rate Estimation

References

• Abramson , I. ( 1982a ). On bandwidth variation in kernel estimates – a square root law . Ann. Statist. 10 ( 4 ): 1217 – 1223 .
   Web of Science ®Google Scholar
• Abramson , I. ( 1982b ). Arbitrariness of the pilot estimator in adaptive kernel methods . J. Multivariate Anal. 12 : 562 – 567 .
   Web of Science ®Google Scholar
• Bagkavos , D. ( 2003 ). Bias Reduction in Nonparametric Hazard Rate Estimation . PhD thesis , The University of Birmingham , UK .
   Google Scholar
• Burkholder , D. L. ( 1973 ). Distribution function inequalities for martingales . Ann. Probab. 1 : 19 – 42 .
   Web of Science ®Google Scholar
• González-Manteiga , W. , Cao , R. , Marron , J. S. ( 1996 ). Bootstrap selection of the smoothing parameter in nonparametric hazard rate estimation . J. Amer. Statist. Assoc. 91 : 1130 – 1140 .
   Web of Science ®Google Scholar
• Hajek , J. ( 1968 ). Asymptotic normality of simple linear statistics under alternatives . Ann. Mathemat. Statist. 39 : 325 – 346 .
   Google Scholar
• Hall , P. ( 1990 ). On the bias of variable bandwidth curve estimators . Biometrika 77 : 529 – 535 .
   Web of Science ®Google Scholar
• Hall , P. , Heyde , C. ( 1980 ). Martingale Limit Theory and Its Applications . New York : Academic Press .
   Google Scholar
• Hall , P. , Marron , J. S. ( 1988 ). Variable window width kernel estimates of probability densities . Probab. Theor. Related Fields 80 : 37 – 49 .
   Web of Science ®Google Scholar
• Hall , P. , Hu , T. C. , Marron , J. S. ( 1995 ). Improved variable window width kernel estimates of probability densities . Ann. Statist. 23 : 1 – 10 .
   Web of Science ®Google Scholar
• Hazelton , M. L. ( 2007 ). Bias reduction in kernel binary regression . Computat. Statist. Data Anal. 51 : 4393 – 4402 .
   Google Scholar
• Jones , M. C. , Signorini , D. F. ( 1997 ). A comparison of higher order bias kernel density estimators . J. Amer. Statist. Assoc. 91 ( 433 ): 401 – 407 .
   Google Scholar
• Jones , M. C. , Marron , S. , Sheather , S. ( 1996 ). A brief survey of bandwidth selection for density estimation . J. Amer. Statist. Assoc. 92 ( 439 ): 1063 – 1073 .
   Google Scholar
• Lo , Y. , Mack , S. , Wang , J. ( 1989 ). Density and hazard rate estimation for censored data via strong representation of the Kaplan–Meyer estimator . Probab. Theor. Related Fields 80 : 461 – 473 .
   Web of Science ®Google Scholar
• Müller , H.-G. , Wang , J. L. ( 1994 ). Hazard rate estimation under random censoring with varying kernels and bandwidths . Biometrics 50 : 61 – 76 .
   PubMed Web of Science ®Google Scholar
• Nielsen , J. P. ( 2003 ). Variable bandwidth kernel hazard estimators . Nonparametric Statist. 15 ( 3 ): 355 – 376 .
   Web of Science ®Google Scholar
• Patil , P. N. ( 1993 ). Bandwidth choice for non parametric hazard rate estimation . J. Statist. Plann. Infer. 35 : 15 – 30 .
   Google Scholar
• Rice , J. , Rosenblatt , M. ( 1976 ). Estimation of the log-survivor function and hazard function . Sankhya, Ser. A 38 : 60 – 78 .
   Google Scholar
• Ruppert , D. , Cline , D. ( 1994 ). Bias reduction in kernel density estimation by smoothed empirical transformations . Ann. Statist. 22 ( 1 ): 185 – 210 .
   Google Scholar
• Sarda , P. , Vieu , P. ( 1991 ). Smoothing parameter selection in hazard rate estimation . Statist. Probab. Lett. 11 : 429 – 434 .
   Web of Science ®Google Scholar
• Silverman , B. ( 1986 ). Density Estimation for Statistics and Data Analysis . London : Chapman & Hall .
   Google Scholar
• Simonoff , J. ( 1996 ). Smoothing Methods in Statistics . New York : Springer .
   Google Scholar
• Stone , C. J. ( 1984 ). An asymptotically optimal window selection rule for kernel density estimates . Ann. Statist. 12 : 1285 – 1297 .
   Web of Science ®Google Scholar
• Tanner , M. (1983). A note on the variable kernel estimator of the hazard function from randomly censored data. Ann. Statist. 11:994–998.
   Web of Science ®Google Scholar
• Tanner , M. , Wong , W. ( 1983 ). The estimation of the hazard function from randomly censored data by the kernel method . Ann. Statist. 11 : 989 – 993 .
   Web of Science ®Google Scholar
• Wand , M. P. , Jones , M. C. ( 1995 ). Kernel Smoothing . London : Chapman and Hall .
   Google Scholar
• Watson , G. , Leadbetter , M. ( 1964 ). Hazard analysis I . Biometrika 51 : 175 – 184 .
   Web of Science ®Google Scholar