IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v216y2025ics0167715224002128.html

Unified specification tests in partially linear quantile regression models

Author

Listed:
  • Song, Xiaojun
  • Yang, Zixin

Abstract

We propose specification tests for parametric quantile regression models versus semiparametric alternatives over a continuum of quantile levels. The test statistics are constructed as continuous functionals of a quantile-marked residual process. We show that using an orthogonal projection on the tangent space of nuisance parameters at each quantile index delivers unified asymptotic properties for tests based on different estimators. Consistency of the tests and asymptotic power under a sequence of local alternatives converging to the null at a parametric rate are also discussed. We propose a simple multiplier bootstrap procedure to carry out the tests, whose nominal levels are well approximated in our simulation study for modest sample sizes.

Suggested Citation

  • Song, Xiaojun & Yang, Zixin, 2025. "Unified specification tests in partially linear quantile regression models," Statistics & Probability Letters, Elsevier, vol. 216(C).
    • Handle: RePEc:eee:stapro:v:216:y:2025:i:c:s0167715224002128
    DOI: 10.1016/j.spl.2024.110243
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167715224002128
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.spl.2024.110243?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Zhongjun Qu & Jungmo Yoon & Pierre Perron, 2024. "Inference on Conditional Quantile Processes in Partially Linear Models with Applications to the Impact of Unemployment Benefits," The Review of Economics and Statistics, MIT Press, vol. 106(2), pages 521-541, March.
    2. Yiguo Sun & Thanasis Stengos, 2008. "The absolute health income hypothesis revisited: a semiparametric quantile regression approach," Empirical Economics, Springer, vol. 35(2), pages 395-412, September.
    3. Lee, Sokbae, 2003. "Efficient Semiparametric Estimation Of A Partially Linear Quantile Regression Model," Econometric Theory, Cambridge University Press, vol. 19(1), pages 1-31, February.
    4. Escanciano, J.C. & Goh, S.C., 2014. "Specification analysis of linear quantile models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 495-507.
    5. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    6. Wangli Xu & Xu Guo & Lixing Zhu, 2012. "Goodness-of-fitting for partial linear model with missing response at random," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(1), pages 103-118.
    7. Escanciano, Juan Carlos & Velasco, Carlos, 2010. "Specification tests of parametric dynamic conditional quantiles," Journal of Econometrics, Elsevier, vol. 159(1), pages 209-221, November.
    8. Feng, Xingdong & Liu, Qiaochu & Wang, Caixing, 2023. "A lack-of-fit test for quantile regression process models," Statistics & Probability Letters, Elsevier, vol. 192(C).
    9. Matthew Harding & Carlos Lamarche, 2017. "Penalized Quantile Regression with Semiparametric Correlated Effects: An Application with Heterogeneous Preferences," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 32(2), pages 342-358, March.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Xiaojun Song & Jichao Yuan, 2026. "A Projection Approach to Nonparametric Significance and Conditional Independence Testing," Papers 2602.15289, arXiv.org.
    2. Xiaojun Song & Jichao Yuan, 2025. "Specification tests for regression models with measurement errors," Papers 2511.04127, arXiv.org.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Conde-Amboage, Mercedes & Sánchez-Sellero, César & González-Manteiga, Wenceslao, 2015. "A lack-of-fit test for quantile regression models with high-dimensional covariates," Computational Statistics & Data Analysis, Elsevier, vol. 88(C), pages 128-138.
    2. Gimenes, Nathalie & Guerre, Emmanuel, 2022. "Quantile regression methods for first-price auctions," Journal of Econometrics, Elsevier, vol. 226(2), pages 224-247.
    3. Qu, Zhongjun & Yoon, Jungmo, 2015. "Nonparametric estimation and inference on conditional quantile processes," Journal of Econometrics, Elsevier, vol. 185(1), pages 1-19.
    4. Charlier, Isabelle & Paindaveine, Davy & Saracco, Jérôme, 2015. "Conditional quantile estimation based on optimal quantization: From theory to practice," Computational Statistics & Data Analysis, Elsevier, vol. 91(C), pages 20-39.
    5. Fan, Yanqin & Liu, Ruixuan, 2016. "A direct approach to inference in nonparametric and semiparametric quantile models," Journal of Econometrics, Elsevier, vol. 191(1), pages 196-216.
    6. Liyun Zhou & Weinan Lin & Chunpeng Yang, 2024. "Investor trading behavior and asset prices: Evidence from quantile regression analysis," International Journal of Finance & Economics, John Wiley & Sons, Ltd., vol. 29(2), pages 1722-1744, April.
    7. Pereda-Fernández, Santiago, 2023. "Identification and estimation of triangular models with a binary treatment," Journal of Econometrics, Elsevier, vol. 234(2), pages 585-623.
    8. Zongwu Cai & Meng Shi & Yue Zhao & Wuqing Wu, 2020. "Testing Financial Hierarchy Based on A PDQ-CRE Model," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202011, University of Kansas, Department of Economics, revised Jul 2020.
    9. Battagliola, Maria Laura & Sørensen, Helle & Tolver, Anders & Staicu, Ana-Maria, 2022. "A bias-adjusted estimator in quantile regression for clustered data," Econometrics and Statistics, Elsevier, vol. 23(C), pages 165-186.
    10. Yiguo Sun & Thanasis Stengos, 2008. "The absolute health income hypothesis revisited: a semiparametric quantile regression approach," Empirical Economics, Springer, vol. 35(2), pages 395-412, September.
    11. Escanciano, J.C. & Goh, S.C., 2014. "Specification analysis of linear quantile models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 495-507.
    12. Graham, Bryan S. & Hahn, Jinyong & Poirier, Alexandre & Powell, James L., 2018. "A quantile correlated random coefficients panel data model," Journal of Econometrics, Elsevier, vol. 206(2), pages 305-335.
    13. Zongwu Cai & Ying Fang & Ming Lin & Shengfang Tang, 2021. "A Nonparametric Test for Testing Heterogeneity in Conditional Quantile Treatment Effects," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202117, University of Kansas, Department of Economics, revised Aug 2021.
    14. Wu, Chaojiang & Yu, Yan, 2014. "Partially linear modeling of conditional quantiles using penalized splines," Computational Statistics & Data Analysis, Elsevier, vol. 77(C), pages 170-187.
    15. Sun, Yiguo, 2006. "A Consistent Nonparametric Equality Test Of Conditional Quantile Functions," Econometric Theory, Cambridge University Press, vol. 22(4), pages 614-632, August.
    16. Panayiotis Tzeremes, 2022. "The Asymmetric Effects of Regional House Prices in the UK: New Evidence from Panel Quantile Regression Framework," Studies in Microeconomics, , vol. 10(1), pages 7-22, June.
    17. Nieto, Maria Rosa & Ruiz, Esther, 2016. "Frontiers in VaR forecasting and backtesting," International Journal of Forecasting, Elsevier, vol. 32(2), pages 475-501.
    18. Ana Pérez-González & Tomás R. Cotos-Yáñez & Wenceslao González-Manteiga & Rosa M. Crujeiras-Casais, 2021. "Goodness-of-fit tests for quantile regression with missing responses," Statistical Papers, Springer, vol. 62(3), pages 1231-1264, June.
    19. Haowen Bao & Zongwu Cai & Yuying Sun & Shouyang Wang, 2023. "Penalized Optimal Forecast Combination for Quantile Regressions," WORKING PAPERS SERIES IN THEORETICAL AND APPLIED ECONOMICS 202514, University of Kansas, Department of Economics, revised May 2025.
    20. Christoph Breunig, 2019. "Specification Testing in Nonparametric Instrumental Quantile Regression," Papers 1909.10129, arXiv.org.

    More about this item

    Keywords

    ;
    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:stapro:v:216:y:2025:i:c:s0167715224002128. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.elsevier.com/wps/find/journaldescription.cws_home/622892/description#description .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.