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A lack-of-fit test for quantile regression process models

Author

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  • Feng, Xingdong
  • Liu, Qiaochu
  • Wang, Caixing

Abstract

Quantile regression is a widely used statistical tool for data analysis in practice, but model misspecifications may lead to incorrect inferences. In this paper, a lack-of-fit test for quantile regression processes is proposed for those cases with multivariate covariates, which has not been well studied in the existing literature. An asymptotic result is established, and a numerical study has demonstrated that the proposed method is promising.

Suggested Citation

  • Feng, Xingdong & Liu, Qiaochu & Wang, Caixing, 2023. "A lack-of-fit test for quantile regression process models," Statistics & Probability Letters, Elsevier, vol. 192(C).
  • Handle: RePEc:eee:stapro:v:192:y:2023:i:c:s0167715222001936
    DOI: 10.1016/j.spl.2022.109680
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    References listed on IDEAS

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    1. Bo Kai & Runze Li & Hui Zou, 2010. "Local composite quantile regression smoothing: an efficient and safe alternative to local polynomial regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(1), pages 49-69, January.
    2. Yanliang Chen & Man-Lai Tang & Maozai Tian, 2015. "Semiparametric Hierarchical Composite Quantile Regression," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(5), pages 996-1012, March.
    3. Belloni, Alexandre & Chernozhukov, Victor & Chetverikov, Denis & Fernández-Val, Iván, 2019. "Conditional quantile processes based on series or many regressors," Journal of Econometrics, Elsevier, vol. 213(1), pages 4-29.
    4. Qu, Zhongjun & Yoon, Jungmo, 2015. "Nonparametric estimation and inference on conditional quantile processes," Journal of Econometrics, Elsevier, vol. 185(1), pages 1-19.
    5. Chen Dong & Guodong Li & Xingdong Feng, 2019. "Lack‐of‐fit tests for quantile regression models," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 81(3), pages 629-648, July.
    6. Escanciano, J.C. & Goh, S.C., 2014. "Specification analysis of linear quantile models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 495-507.
    7. Guo, Jie & Tang, Manlai & Tian, Maozai & Zhu, Kai, 2013. "Variable selection in high-dimensional partially linear additive models for composite quantile regression," Computational Statistics & Data Analysis, Elsevier, vol. 65(C), pages 56-67.
    8. Baringhaus, L. & Franz, C., 2004. "On a new multivariate two-sample test," Journal of Multivariate Analysis, Elsevier, vol. 88(1), pages 190-206, January.
    9. Lian, Heng & Meng, Jie & Fan, Zengyan, 2015. "Simultaneous estimation of linear conditional quantiles with penalized splines," Journal of Multivariate Analysis, Elsevier, vol. 141(C), pages 1-21.
    10. He X. & Zhu L-X., 2003. "A Lack-of-Fit Test for Quantile Regression," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 1013-1022, January.
    11. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    12. Leucht, Anne & Neumann, Michael H., 2009. "Consistency of general bootstrap methods for degenerate U-type and V-type statistics," Journal of Multivariate Analysis, Elsevier, vol. 100(8), pages 1622-1633, September.
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