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Non-crossing weighted kernel quantile regression with right censored data

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Abstract

Regarding survival data analysis in regression modeling, multiple conditional quantiles are useful summary statistics to assess covariate effects on survival times. In this study, we consider an estimation problem of multiple nonlinear quantile functions with right censored survival data. To account for censoring in estimating a nonlinear quantile function, weighted kernel quantile regression (WKQR) has been developed by using the kernel trick and inverse-censoring-probability weights. However, the individually estimated quantile functions based on the WKQR often cross each other and consequently violate the basic properties of quantiles. To avoid this problem of quantile crossing, we propose the non-crossing weighted kernel quantile regression (NWKQR), which estimates multiple nonlinear conditional quantile functions simultaneously by enforcing the non-crossing constraints on kernel coefficients. The numerical results are presented to demonstrate the competitive performance of the proposed NWKQR over the WKQR.

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Acknowledgments

The authors are grateful to the editor, the associate editor, and the reviewers for their constructive and insightful comments and suggestions, which helped to dramatically improve the quality of this paper. This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by (1) the Ministry of Science, ICT and Future Planning (NRF-2013R1A1A1007536) for S. Bang, (2) the Ministry of Education (NRF-2013R1A1A2A10007545) for M. Jhun, and (3) the Ministry of Education, Science and Technology (2010-0007936) for H. Cho.

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Authors and Affiliations

  1. Department of Mathematics, Korea Military Academy, P.O. Box 77, Seoul, Republic of Korea

    Sungwan Bang

  2. Department of Statistics, Korea University, Seoul, 136-701, Republic of Korea

    Soo-Heang Eo, Myoungshic Jhun & HyungJun Cho

  3. Department of Pathology, Asan Medical Center, Seoul, 138-736, Republic of Korea

    Yong Mee Cho

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  1. Sungwan Bang
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  2. Soo-Heang Eo
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  3. Yong Mee Cho
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  4. Myoungshic Jhun
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  5. HyungJun Cho
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Correspondence to HyungJun Cho.

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Bang, S., Eo, SH., Cho, Y.M. et al. Non-crossing weighted kernel quantile regression with right censored data. Lifetime Data Anal 22, 100–121 (2016). https://doi.org/10.1007/s10985-014-9314-8

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  • DOI: https://doi.org/10.1007/s10985-014-9314-8

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