Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
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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
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Abstract

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.

Keywords

References

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