An estimation of the treatment eect for the right censored data

  • Park, Hyo-Il (Department of Statistics, Chong-ju University) ;
  • Kim, Ju-Sung (Department of Informational Statistics, Chungbuk National University)
  • 투고 : 2011.01.22
  • 심사 : 2011.03.28
  • 발행 : 2011.05.31

초록

In this article, we propose an estimation procedure for the treatment eect for the right censored data. We apply the least square method for deriving the estimation equation and obtain an explicit formula for an estimation. Then we consider some asymptotic properties with derivation of the asymptotic normality for the estimate. Finally we illustrate our procedure with an example and discuss some interesting aspects for the estimation procedure.

키워드

참고문헌

  1. Akritas, M. G. (1986). Empirical processes associated with V-statistics and a class of estimators under random censoring. Annals of Statistics, 14, 619-637. https://doi.org/10.1214/aos/1176349942
  2. Bassiakos, Y. C., Meng, X.-L. and Lo, S.-H. (1991). A general estimator of the treatment effect when the data are heavily censored. Biometrika, 78, 741-748. https://doi.org/10.1093/biomet/78.4.741
  3. Bickel, P. J. and Doksum, K. A. (1977). Mathematical statistics, basic ideas and selected topics, Holden-Day, San Francisco.
  4. Buckley, J. and James, I. (1979). Linear regression with censored data. Biometrika, 66, 429-436. https://doi.org/10.1093/biomet/66.3.429
  5. Chung, K. L. (1974). A course in probability theory, 2nd. Ed., Academic Press, New York.
  6. Cox, D. R. (1972). Regression models and life-tables. Journal of Royal Statistical Society Series B, 34, 187-202.
  7. Feller, W. (1971). An introduction to probability theory and its applications, Volume II, 2nd Ed., Wiley, New York.
  8. Gill, R. D. (1983). Large sample behaviour of the product-limit estimator on the whole line. Annals of Statistics, 11, 49-58. https://doi.org/10.1214/aos/1176346055
  9. Kalbfleisch, J. D. and Prentice, R. L. (1980). The statistical analysis of failure time data, Wiley, New York.
  10. Kaplan, E. and Meier, R. (1958). Nonparametric estimation from incomplete observations. Journal of American Statistical Association, 53, 457-481. https://doi.org/10.1080/01621459.1958.10501452
  11. Meng, X.-L., Bassiakos, Y. and Lo, S.-H. (1991). Large-sample properties for a general estimator of the treatment effect in the two-sample problem with right censoring. Annals of Statistics, 19, 1786-1812. https://doi.org/10.1214/aos/1176348371
  12. Miller, R. G. (1976). Least squares regression with censored data. Biometrika, 63, 449-464. https://doi.org/10.1093/biomet/63.3.449
  13. Park, H.-I. and Park, S.-G. (1995). Quantile estimation of treatment e ect for the two-sample problem with right censored data. Statistics & Probability Letters, 24, 139-145. https://doi.org/10.1016/0167-7152(94)00158-5
  14. Pike, M. C. (1966). A method of analysis of certain class of experiments in carcinogenesis. Biometrics, 22, 142-161. https://doi.org/10.2307/2528221
  15. Shorack, G. R. and Wellner, J. A. (1986). Empirical processes with applications to statistics, Wiley, New York.
  16. Tsiatis, A. A. (1990). Estimating regression parameters using linear rank tests for censored data. Annals of Statistics, 18, 354-372. https://doi.org/10.1214/aos/1176347504
  17. Zhou, Y. and Liang, H. (2005). Empirical-likelihood-based semiparametric inference for the treatment effect in the two-sample problem with censoring. Biometrika, 92, 271-282. https://doi.org/10.1093/biomet/92.2.271