中国科学院数学与系统科学研究院期刊网

Acta Mathematicae Applicatae Sinica(English Series) >

2025 , Vol. 41 >Issue 2: 479 - 497

DOI: https://doi.org/10.1007/s10255-024-1034-6

ARTICLES

Quantile Regression under Truncated, Censored and Dependent Assumptions

  • Chang-sheng LIU ,
  • Yun-jiao LU ,
  • Si-li NIU
Expand
  • 1 School of Mathematics and Physics, Henan University of Urban Construction, Pingdingshan 467036, China;
    2 School of Mathematical Sciences, Tongji University, Shanghai 200092, China

Received date: 2022-03-02

  Accepted date: 2022-10-12

  Online published: 2025-03-28

Supported by

The work is supported by the National Natural Science Foundation of China (12071348), the Key Scientific Research Foundation of Henan Educational Committee (24A110001) and Key Laboratory of Intelligent Computing and Applications (Ministry of Education), Tongji University, China.

Fold

Abstract

In this paper, we focus on the problem of nonparametric quantile regression with left-truncated and right-censored data. Based on Nadaraya-Watson (NW) Kernel smoother and the technique of local linear (LL) smoother, we construct the NW and LL estimators of the conditional quantile. Under strong mixing assumptions, we establish asymptotic representation and asymptotic normality of the estimators. Finite sample behavior of the estimators is investigated via simulation, and a real data example is used to illustrate the application of the proposed methods.

Key words： asymptotic normality; asymptotic representation; nonparametric quantile regression; truncated and censored; $\alpha$-mixing

Cite this article

Chang-sheng LIU , Yun-jiao LU , Si-li NIU . Quantile Regression under Truncated, Censored and Dependent Assumptions[J]. Acta Mathematicae Applicatae Sinica(English Series), 2025 , 41(2) : 479 -497 . DOI: 10.1007/s10255-024-1034-6

References

[1] Bang, H., Tsiatis, A. A. Median regression with censored cost data. Biometrics, 58(3): 643-649(2002)
[2] Buhamra, S. S., Al-Kandari, N. M., Ahmed, S. E. Nonparametric inference strategies for the quantile functions under left truncation and right censoring. J. Nonparametr. Stat., 19(4-5): 189-198(2007)
[3] Cai, J., Kim, J. Nonparametric quantile estimation with correlated failure time data. Lifetime Data Anal., 9(4): 357-371(2003)
[4] Cai, Z. Estimating a distribution function for censored time series data. J. Multivariate Anal., 78(2): 299-318(2001)
[5] Cai, Z. Regression quantiles for time series. Econometric Theory, 18: 169-192(2002)
[6] Cheng, J.-Y., Huang, S.-C., Tzeng, S.-J. Quantile regression methods for left-truncated and right-censored data. J. Stat. Comput. Simul., 86(3): 443-459(2016)
[7] Chernozhukov, V., Hong, H. Three-step censored quantile regression and extramarital affairs. J. Amer. Statist. Assoc., 97(459): 872-882(2002)
[8] Doukhan P. Mixing: properties and examples. Springer Science & Business Media, New York, 2012
[9] El Ghouch, A., Van Keilegom, I. Local linear quantile regression with dependent censored data. Statist. Sinica, 19: 1621-1640(2009)
[10] Fan, J., Gijbels, I. Local polynomial modelling and its applications. Chapman and Hall, London, 1996
[11] Fan, J., Yao, Q. Nonlinear Time Series. Springer, New York, 2003
[12] Frumento, P., Bottai, M. An estimating equation for censored and truncated quantile regression. Comput. Statist. Data Anal., 113: 53-63(2017)
[13] Gannoun, A., Saracco, J., Yu, K. Nonparametric prediction by conditional median and quantiles. J. Statist. Plann. Inference, 117(2), 207-223(2003)
[14] Hall, P., Heyde, C. C. Martingale Limit Theory and Its Application. Academic Press, New York, 1980
[15] He, S., Yang, G. Estimation of regression parameters with left truncated data. J. Statist. Plann. Inference, 117: 99-12(2003)
[16] Iglesias-Pérez, M. C. Strong representation of a conditional quantile function estimator with truncated and censored data. Statist. Probab. Lett., 65(2): 79-91(2003)
[17] Iglesias-Pérez, C., González-Manteiga, W. Strong representation of a generalized product-limit estimator for truncated and censored data with some applications. J. Nonparametr. Stat., 10(3): 213-244(1999)
[18] Ji, S., Peng, L., Cheng, Y., Lai, H. Quantile regression for doubly censored data. Biometrics, 68(1): 101-112(2012)
[19] Knight, K. Limiting distributions for l1 regression estimators under general conditions. Ann. Statist., 26(2): 755-770(1998)
[20] Koenker, R., Bassett, G. J. Regression quantiles. Econometrica, 46: 33-50(1978)
[21] Koenker, R. Quantile Regression. Cambridge University Press, Cambridge, 2005
[22] Kohler, M., Tent, R. Nonparametric quantile estimation using surrogate models and importance sampling. Metrika, 83(2): 141-169(2020)
[23] Li, R., Peng, L. Quantile regression for left-truncated semicompeting risks data. Biometrics, 67(3): 701-710(2011)
[24] Lipsitz, S. R., Ibrahim, J. G. Estimation with correlated censored survival data with missing covariates. Biostatistics, 1: 315-327(2000)
[25] Liang, H. Y., de Uña-Álvarez, J., Iglesias-Pérez, M. C. Asymptotic properties of conditional distribution estimator with truncated, censored and dependent data. Test, 21(4): 790-810(2012)
[26] Sankaran, P. G., Unnikrishnan Nair, N. Nonparametric estimation of hazard quantile function. J. Nonparametr. Stat., 21(6): 757-767(2009)
[27] Shen, P. S. A weighted quantile regression for left-truncated and right-censored data. J. Stat. Comput. Simul., 84(3): 596-604(2014)
[28] Volkonskii, V. A., Rozanov, Y. A. Some limit theorems for random functions. Theor. Probability Appl., 4(2): 178-197(1959)
[29] Wang, H. J., Wang, L. Locally weighted censored quantile regression. J. Amer. Statist. Assoc., 104(487): 1117-1128(2009)
[30] Xu, H. X., Chen, Z. L., Wang, J. F., Fan, G. L. Quantile regression and variable selection for partially linear model with randomly truncated data. Statist. Papers, 60(4): 1137-1160(2019)
[31] Xu, H. X., Fan, G. L., Chen, Z. L., Wang, J. F. Weighted quantile regression and testing for varyingcoefficient models with randomly truncated data. AStA Adv. Stat. Anal., 102(4): 565-588(2018)
[32] Yin, G., Cai, J. Quantile regression models with multivariate failure time data. Biometrics, 61: 151-161(2005)
[33] Yu, K., Jones, M. Local linear quantile regression. J. Amer. Statist. Assoc., 93(441): 228-237(1998)
[34] Zhou, W. A weighted quantile regression for randomly truncated data. Comput. Statist. Data Anal., 55(1): 554-566(2011)
Options
Outlines

/

〈 〉