Quantile calculus and censored regression

Annals of Statistics

Volumn 38, Issue 3, 2010, Pages 1607-1637

  Huang, Yijian ^a  

^a EMORY UNIVERSITY   (United States)

Author keywords

Differential equation; Estimating integral equation; Piecewise linear programming; PLMIN algorithm; Quantile equality fraction; Regression quantile; Relative quantile; Varying coefficient model

Indexed keywords

EID: 77951439473     PISSN: 00905364     EISSN: None     Source Type: Journal    
DOI: 10.1214/09-AOS771     Document Type: Article

References (29)

1. AALEN, O. O. (1980). A model for nonparametric regression analysis of counting processes. In Mathematical Statistics and Probability Theory (Proc. Sixth Internat. Conf., Wisla, 1978). (W. Klonecki, A. Kozek and J. Rosiński, eds.). Lecture Notes in Statist. 2 1-25. Springer, New York. MR0577267
2. BUCKLEY, J. and JAMES, I. (1979). Linear regression with censored data. Biometrika 66 429-436.
3. CHERNOZHUKOV, V. (2005). Extremal quantile regression. Ann. Statist. 33 806-839. MR2163160
4. EFRON, B. (1967). The two sample problem with censored data. In Proc. Fifth Berkeley Symp. Math. Statist. Probab. 4 831-853. Prentice Hall, New York.
5. FLEMING, T. R. andHARRINGTON, D. P. (1991). Counting Processes and Survival Analysis.Wiley, New York. MR1100924
6. GILL, P. E., MURRAY, W. andWRIGHT, M. H. (1991). Numerical Linear Algebra and Optimization. Addison-Wesley, Redwood City, CA. MR1074004
7. GILL, R. D. and JOHANSEN, S. (1990). A survey of product-integration with a view towards application in survival analysis. Ann. Statist. 18 1501-1555. MR1074422
8. GUTENBRUNNER, C. and JUREC? KOVÁ, J. (1992). Regression rank scores and regression quantiles. Ann. Statist. 20 305-330. MR1150346
9. HONORÉ, B., KHAN, S. and POWELL, J. L. (2002). Quantile regression under random censoring. J. Econometrics 109 67-105. MR1899693
10. JIN, Z., YING, Z. andWEI, L. J. (2001). A simple resampling method by perturbing the minimand. Biometrika 88 381-390. MR1844838
11. KOENKER, R. (2008). Censored quantile regression redux. J. Stat. Softw. 27 1-25.
12. KOENKER, R. andBASSETT, G. (1978). Regression quantiles. Econometrica 46 33-50. MR0474644
13. KOENKER, R. and D'OREY, V. (1987). Computing regression quantiles. Appl. Statist. 36 383-393.
14. KOENKER, R. and GELING, O. (2001). Reappraising medfly longevity: A quantile regression survival analysis. J. Amer. Statist. Assoc. 96 458-468. MR1939348
15. KOSOROK, M. R. (2008). Introduction to Empirical Processes and Semiparametric Inference. Springer, New York.
16. NEOCLEOUS, T., VANDEN BRANDEN, K. and PORTNOY, S. (2006). Correction to "Censored regression quantiles," by S. Portnoy. J. Amer. Statist. Assoc. 101 860-861. MR2281250
17. OWEN, A. (1990). Empirical likelihood ratio confidence regions. Ann. Statist. 18 90-120. MR1041387
18. PENG, L. and HUANG, Y. (2007). Survival analysis with temporal covariate effects. Biometrika 94 719-733. MR2410019
19. PENG, L. andHUANG, Y. (2008). Survival analysis with quantile regression models. J. Amer. Statist. Assoc. 103 637-649. MR2435468
20. PORTNOY, S. (2003). Censored regression quantiles. J. Amer. Statist. Assoc. 98 1001-1012. MR2041488
21. PORTNOY, S. and JUREC? KOVÁ, J. (1999). On extreme regression quantiles. Extremes 2 227-243. MR1781938
22. POWELL, J. L. (1984). Least absolute deviations estimation for the censored regression model. J. Econometrics 25 303-325. MR0752444
23. POWELL, J. L. (1986). Censored regression quantiles. J. Econometrics 32 143-155. MR0853049
24. ROBINS, J. M. and RITOV, Y. (1997). Toward a curse of dimensionality appropriate (CODA) asymptotic theory for semi-parametric models. Stat. Med. 16 285-319.
25. SMITH, R. (1994). Nonregular regression. Biometrika 81 173-183. MR1279665
26. TIAN, L., ZUCKER, D. and WEI, L. J. (2005). On the Cox model with time-varying regression coefficients. J. Amer. Statist. Assoc. 100 172-183. MR2156827
27. TSIATIS, A. A. (1990). Estimating regression parameters using linear rank tests for censored data. Ann. Statist. 18 354-372. MR1041397
28. WANG, H. J. andWANG, L. (2009). Locally weighed censored quantile regression. J. Amer. Statist. Assoc. 104 1117-1128. MR2562007
29. YING, Z., JUNG, S. H. and WEI, L. J. (1995). Survival analysis with median regression models. J. Amer. Statist. Assoc. 90 178-184. MR1325125