Efficient Score Estimation and Adaptive Rank and M-estimators from Left-Truncated and Right-Censored Data

  • Chul-Ki Kim (Assistant Professor, Department of Statistics, Ewha Womans University, Seoul, 120-750 , Korea)
  • Published : 1996.12.01


Data-dependent (adaptive) choice of asymptotically efficient score functions for rank estimators and M-estimators of regression parameters in a linear regression model with left-truncated and right-censored data are developed herein. The locally adaptive smoothing techniques of Muller and Wang (1990) and Uzunogullari and Wang (1992) provide good estimates of the hazard function h and its derivative h' from left-truncated and right-censored data. However, since we need to estimate h'/h for the asymptotically optimal choice of score functions, the naive estimator, which is just a ratio of estimated h' and h, turns out to have a few drawbacks. An altermative method to overcome these shortcomings and also to speed up the algorithms is developed. In particular, we use a subroutine of the PPR (Projection Pursuit Regression) method coded by Friedman and Stuetzle (1981) to find the nonparametric derivative of log(h) for the problem of estimating h'/h.



  1. J. Econometrics v.15 Linear regression after selection Goldberger, A.S.
  2. Proc. Natl. Acad. Sci, USA v.72 Observational validation of the chronometric cosmology. Ⅰ. Preliminaries and the redshift Segal, I.E.
  3. Statistica Sinica v.2 Asymptotically efficient estimation in censored and truncated regression Lai, T.L.;Ying, Z.
  4. Ann. Statist. v.11 Information and asymptotic efficiency in parametric nonparametric models Begun, J.M.;Hall, W.J.;Huang, W.M.;Wellner, J.A.
  5. Statistical Models and Methods for Lifetime Data Lawless, J.F.
  6. Ann. Statist. v.19 Rank regression methods for left-truncated and right-censored data Lai, T.L.;Ying, Z.
  7. The Statistical Analysis of Failure Time Data Kalbfleisch, J.D.;Prentice, R.L.
  8. Ann. Statist v.22 A missing information principle and M-estimators in regression analysis with censored and Lai, T.L.;Ying, Z.
  9. Technometrics v.14 Theory and applications of hazard piotting for censored failure data Nelson, W.
  10. Astron. Astrophy. v.82 Nonparametric estimation of the observational cutoff bias Nicoll, J.F.;Segal, I.E.
  11. J. Am. Statis. Assoc. v.76 projection pursuit regression Friedman, J.H.
  12. Advanced Econometrics Amemiya, T.
  13. Biometrika v.79 A comparison of hazard rate estimators for left-truneated and right-censored data Uzunogullari, U.;Wang, J.L.
  14. Econometrica v.26 Estimation of relationship for limited dependent variables Tobin, J.
  15. Tech. Report. L95-6 Generalized Additive Models for Left-Truncated and Right-Censored Data Kim, C.K.;Lai, T.L.
  16. Probab. Theory Related Fields v.85 Locally adaptive hazard smoothing Muller, H.G.;Wang, J.L.
  17. Tech. Report. L94-2 Nonparametric estimation and regression analysis with left-truncated and right-censored data Gross, S.;Lai, T.L.