Smoothed and Corrected Score Approach to Censored Quantile Regression With Measurement Errors

REFERENCES

• Bang, H., and Tsiatis, A.A. (2002), “Median Regression With Censored Cost Data,” Biometrics, 58, 643–649.
   PubMed Web of Science ®Google Scholar
• Brown, M.L. (1982), “Robust Line Estimation With Error in Both Variables,” Journal of the American Statistical Association, 77, 71–79. Correction in 78, 1008.
   Web of Science ®Google Scholar
• Buchinsky, M., and Hahn, J.Y. (1998), “An Alternative Estimator for Censored Quantile Regression,” Econometrica, 66, 653–671.
   Web of Science ®Google Scholar
• Buckley, J., and James, I. (1979), “Linear Regression With Censored Data,” Biometrika, 66, 429–436.
   Web of Science ®Google Scholar
• Carroll, R.J., Ruppert, D., Stefanski, L.A., and Crainiceanu, C. (2006), Measurement Error in Nonlinear Models: A Modern Perspective, London: CRC Press.
   Google Scholar
• Chernozhukov, V., and Hong, H. (2002), “Three-Step Censored Quantile Regression and Extramarital Affairs,” Journal of the American Statistical Association, 97, 872–882.
   Web of Science ®Google Scholar
• Cox, D.R. (1972), “Regression Models and Life Tables” (with discussion), Journal of Royal Statistical Society, Series B, 34, 187–220.
   Web of Science ®Google Scholar
• Fitzenberger, B. (1997), “A Guide to Censored Quantile Regressions,” in Handbook of Statistics, Robust Inference, eds. G. S. Maddalaand C. R. Rao, Amsterdam: North-Holland.
   Google Scholar
• Fleming, T.R., and Harrington, D. (1991), Counting Processes and Survival Analysis, New York: Wiley.
   Google Scholar
• He, X., and Liang, H. (2000), “Quantile Regression Estimates for a Class of Linear and Partially Linear Errors-in-Variables Models,” Statistica Sinica, 10, 129–140.
   Web of Science ®Google Scholar
• He, W., Yi, G.Y., and Xiong, J. (2007), “Accelerated Failure Time Models With Covariates Subject to Measurement Error,” Statistics in Medicine, 26, 4817–4832.
   PubMed Web of Science ®Google Scholar
• Hong, H., and Tamer, E. (2003), “A Simple Estimator for Nonlinear Error in Variable Models,” Journal of Econometrics, 117, 1–19.
   Web of Science ®Google Scholar
• Horowitz, J. (1992), “A Smoothed Maximum Score Estimator for the Binary Response Model,” Econometrica, 60, 505–531.
   Web of Science ®Google Scholar
• Horowitz, J. (1998), “Bootstrap Methods for Median Regression Model,” Econometrica, 66, 1327–1352.
   Web of Science ®Google Scholar
• Jin, Z., Lin, D.Y., Wei, L.J., and Ying, Z. (2003), “Rank-Based Inference for the Accelerated Failure Time Model,” Biometrika, 90, 341–353.
   Web of Science ®Google Scholar
• Khan, S., and Powell, L.J. (2001), “Two-Step Estimation of Semiparametric Censored Regression Models,” Journal of Econometrics, 103, 73–110.
   Web of Science ®Google Scholar
• Kocherginsky, M., He, X., and Mu, Y. (2005), “Practical Confidence Intervals for Regression Quantiles,” Journal of Computational and Graphical Statistics, 14, 41–55.
   Web of Science ®Google Scholar
• Koenker, R. (2005), Quantile Regression, New York: Cambridge University Press.
   Google Scholar
• Koenker, R., and Bassett, G.J. (1978), “Regression Quantiles,” Econometrica, 46, 33–50.
   Web of Science ®Google Scholar
• Koenker, R., and Geling, O. (2001), “Reappraising Medfly Longevity: A Quantile Regression Survival Analysis,” Journal of the American Statistical Association, 96, 458–468.
   Web of Science ®Google Scholar
• Kotz, S., Kozubowski, T.J., and Podgorski, K. (2001), The Laplace Distribution and Generalizations, New York: Springer.
   Google Scholar
• Lai, T.L., and Ying, Z. (1991), “Rank Regression Methods for Left-Truncated and Right-Censored Data,” The Annals of Statistics, 19, 531–556.
   Web of Science ®Google Scholar
• Li, Y., and Ryan, L. (2004), “Survival Analysis With Heterogeneous Covariate Measurement Error,” Journal of the American Statistical Association, 99, 724–735.
   Web of Science ®Google Scholar
• Lindgren, A. (1997), “Quantile Regression With Censored Data Using Generalized L1 Minimization,” Computational Statistics and Data Analysis, 23, 509–524.
   Web of Science ®Google Scholar
• Ma, Y., and Yin, G. (2011), “Censored Quantile Regression With Covariate Measurement Errors,” Statistica Sinica, 21, 949–971.
   Web of Science ®Google Scholar
• Nakamura, T. (1990), “Corrected Score Function for Errors-in-Variables Models: Methodology and Application to Generalized Linear Models,” Biometrika, 77, 127–137.
   Web of Science ®Google Scholar
• Peng, L., and Huang, Y. (2008), “Survival Analysis With Quantile Regression Models,” Journal of the American Statistical Association, 103, 637–649.
   Web of Science ®Google Scholar
• Portnoy, S. (2003), “Censored Regression Quantiles,” Journal of the American Statistical Association, 98, 1001–1012.
   Web of Science ®Google Scholar
• Powell, J.L. (1984), “Least Absolute Deviations Estimation for the Censored Regression,” Journal of Econometrics, 25, 303–325.
   Web of Science ®Google Scholar
• Prentice, R.L. (1978), “Linear Rank Tests With Right Censored Data,” Biometrika, 65, 167–180.
   Web of Science ®Google Scholar
• Ritov, Y. (1990), “Estimation in a Linear Regression Model With Censored Data,” The Annals of Statistics, 18, 303–328.
   Web of Science ®Google Scholar
• Stefanski, L.A. (1989), “Unbiased Estimation of a Nonlinear Function of a Normal-Mean With Application to Measurement Error Models,” Communications in Statistics-Theory and Methods, 18, 4335–4358.
   Web of Science ®Google Scholar
• Tsiatis, A.A. (1990), “Estimating Regression Parameters Using Linear Rank Tests for Censored Data,” The Annals of Statistics, 18, 354–372.
   Web of Science ®Google Scholar
• van der Vaart, A.W. (1998), Asymptotic Statistics, New York: Cambridge University Press.
   Google Scholar
• Wang, H., and Wang, L. (2009), “Locally Weighted Censored Quantile Regression,” Journal of the American Statistical Association, 104, 1117–1128.
   Web of Science ®Google Scholar
• Wang, H., Stefanski, L.A., and Zhu, Z. (2012), “Corrected-Loss Estimation for Quantile Regression With Covariate Measurement Errors,” Biometrika, 99, 405–421.
   PubMed Web of Science ®Google Scholar
• Wei, L.J., Ying, Z., and Lin, D.Y. (1990), “Linear Regression Analysis of Censored Survival Data Based on Rank Tests,” Biometrika, 77, 845–851.
   Web of Science ®Google Scholar
• Wei, Y., and Carroll, R.J. (2009), “Quantile Regression With Measurement Error,” Journal of the American Statistical Association, 104, 1129–1143.
   PubMed Web of Science ®Google Scholar
• Yang, S. (1999), “Censored Median Regression Using Weighted Empirical Survival and Hazard Function,” Journal of the American Statistical Association, 94, 137–145.
   Web of Science ®Google Scholar
• Ying, Z., Jung, S.H., and Wei, L.J. (1995), “Survival Analysis With Median Regression Models,” Journal of the American Statistical Association, 90, 178–184.
   Web of Science ®Google Scholar