Communications for Statistical Applications and Methods

The Korean Statistical Society (한국통계학회)
권호 표지
DOI QR코드

DOI QR Code

Regression Quantiles Under Censoring and Truncation

  • Park, Jin-Ho (Department of Statistics, Inha University) ;
  • Kim, Jin-Mi (Department of Statistics, Inha University)
  • Published : 2005.12.01
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper we propose an estimation method for regression quantiles with left-truncated and right-censored data. The estimation procedure is based on the weight determined by the Kaplan-Meier estimate of the distribution of the response. We show how the proposed regression quantile estimators perform through analyses of Stanford heart transplant data and AIDS incubation data. We also investigate the effect of censoring on regression quantiles through simulation study.

Keywords

References

  1. Buchinsky, M. (1995). Estimating the asymptotic covariance matrix for quantile regression models, J. Ecometrics, Vol. 68, 303-338 https://doi.org/10.1016/0304-4076(94)01652-G
  2. Buchinsky, M. and Hahn, J, (1998). An alternative estimator for the censored quantile regression model, Econometrica, Vol. 66, 653-671 https://doi.org/10.2307/2998578
  3. Buckley, J, and James, I. (1979). Linear regression with censored data, Biometrika, Vol. 66, 429-464 https://doi.org/10.1093/biomet/66.3.429
  4. Chen, S. and Khan, S. (2001). Estimation of a partially linear censored regression model, Econometrics Theory, Vol. 17, 567-590 https://doi.org/10.1017/S0266466601173032
  5. Cox, D.R. (1972). Regression models and life-tables (with discussion), J. Roy. Statist. Soc. Ser. B, Vol. 34, 187-220
  6. Gross, S.T. and Lai, T.L. (1996). Nonparametric estimation and regression analysis with left-truncated and right-censored data, J. Amer. Statist. Assoc., Vol. 91, 1166-1180 https://doi.org/10.2307/2291735
  7. Honore, B., Khan, S. and Powell, J.L. (2002). Quantile regression under random censoring, J. Ecometrics, Vol. 109, 67-105 https://doi.org/10.1016/S0304-4076(01)00142-7
  8. Kalbfleisch, J,D. and Lawless, J.F. (1989). Inference based on retrospective ascertainment: An analysis of the data on transfusion-related AIDS, J. Amer. Statist. Assoc., Vol. 84, 360-372 https://doi.org/10.2307/2289919
  9. Koenker, R. and Basset, G. (1978). Regression quantiles, Econometrica, Vol. 46, 33-50 https://doi.org/10.2307/1913643
  10. Koenker, R. and Park, B.J, (1996). An interior point algorithm for nonlinear quantile regression. J. Ecometrics, Vol. 71, 265-283 https://doi.org/10.1016/0304-4076(96)84507-6
  11. Lai, T.L. and Ying, Z. (1991). Estimating a distribution function with truncated and censored data, Ann Statist., Vol. 19, 417-442 https://doi.org/10.1214/aos/1176347991
  12. Leurgans, S. (1987). Linear models, random censoring and synthetic data, Biometrika, Vol. 74, 301-309 https://doi.org/10.1093/biomet/74.2.301
  13. Lindgren, A. (1997). Quantile regression with censored data using generalized$L_1$ minimization, Comput. Statist. Data Anal., Vol. 23, 509-524 https://doi.org/10.1016/S0167-9473(96)00048-5
  14. Miller, R.G. (1976). Least squares regression with censored data, Biometrika, Vol. 63, 449-464 https://doi.org/10.1093/biomet/63.3.449
  15. Newey, W.K. and Powell, J.L. (1990). Efficient estimation of linear and type I censored regression models under conditional quantile restrictions, Econometrics Theory, Vol. 6, 295-317 https://doi.org/10.1017/S0266466600005284
  16. Park, J. and Hwang, J. (2003). Regression depth with censored and truncated data, Comm. Statist., Vol. 32, 997-1008 https://doi.org/10.1081/STA-120019958
  17. Powell, J. (1984). Least absolute deviations estimation for the censored regression model, J. Ecometrics, Vol. 25, 303-325 https://doi.org/10.1016/0304-4076(84)90004-6
  18. Powell, J.(1986). Censored Regression Quantiles, J. Ecometrics, Vol. 32, 143-155 https://doi.org/10.1016/0304-4076(86)90016-3
  19. Portnoy, S. (2003). Censored regression quantiles, J. Amer. Statist. Assoc., Vol. 98, 1001-2003 https://doi.org/10.1198/016214503000000954
  20. Tobin, J. (1958). Estimation of relationships for limited dependent variables, Econometrica, Vol. 26, 24-36 https://doi.org/10.2307/1907382
  21. Ying, Z., Jung, S.H. and Wei, L.J, (1995). Survival analysis with median regression models, J. Amer. Statist. Assoc., Vol. 90, 178-184 https://doi.org/10.2307/2291141
  22. Zhou, M. (1992). M-estimation in censored linear models, Biometrika, Vol. 79, 837-841 https://doi.org/10.1093/biomet/79.4.837