IDEAS home Printed from https://ideas.repec.org/a/eee/stapro/v29y1996i2p107-115.html
   My bibliography  Save this article

Conditional Lp-quantiles and their application to the testing of symmetry in non-parametric regression

Author

Listed:
  • Chen, Zehua

Abstract

The idea of using regression quantiles to test symmetry in a linear regression model is generalized to the non-parametric regression setting. The properties of the Lp-quantiles, defined through an asymmetric Lp-loss function, are derived. The asymptotic normality of the kernel estimates of the conditional Lp-quantiles in the non-parametric regression setting is obtained and their application to the testing of symmetry is discussed.

Suggested Citation

  • Chen, Zehua, 1996. "Conditional Lp-quantiles and their application to the testing of symmetry in non-parametric regression," Statistics & Probability Letters, Elsevier, vol. 29(2), pages 107-115, August.
    • Handle: RePEc:eee:stapro:v:29:y:1996:i:2:p:107-115
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/0167-7152(95)00163-8
    Download Restriction: Full text for ScienceDirect subscribers only
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. Koenker, Roger & Bassett, Gilbert, Jr, 1982. "Robust Tests for Heteroscedasticity Based on Regression Quantiles," Econometrica, Econometric Society, vol. 50(1), pages 43-61, January.
    2. Koenker, Roger W & Bassett, Gilbert, Jr, 1978. "Regression Quantiles," Econometrica, Econometric Society, vol. 46(1), pages 33-50, January.
    3. Antoch, J. & Janssen, P., 1989. "Nonparametric regression M-quantiles," Statistics & Probability Letters, Elsevier, vol. 8(4), pages 355-362, September.
    4. Newey, Whitney K & Powell, James L, 1987. "Asymmetric Least Squares Estimation and Testing," Econometrica, Econometric Society, vol. 55(4), pages 819-847, July.
    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. Daouia, Abdelaati & Girard, Stéphane & Stupfler, Gilles, 2017. "Extreme M-quantiles as risk measures: From L1 to Lp optimization," TSE Working Papers 17-841, Toulouse School of Economics (TSE).
    2. Bellini, Fabio, 2012. "Isotonicity properties of generalized quantiles," Statistics & Probability Letters, Elsevier, vol. 82(11), pages 2017-2024.
    3. Weiwei Li & Dejian Tian, 2023. "Robust optimized certainty equivalents and quantiles for loss positions with distribution uncertainty," Papers 2304.04396, arXiv.org.
    4. Bignozzi, Valeria & Merlo, Luca & Petrella, Lea, 2024. "Inter-order relations between equivalence for Lp-quantiles of the Student's t distribution," Insurance: Mathematics and Economics, Elsevier, vol. 116(C), pages 44-50.
    5. Yingying Jiang & Fuming Lin & Yong Zhou, 2021. "The kth power expectile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 83-113, February.
    6. Daouia, Abdelaati & Paindaveine, Davy, 2019. "Multivariate Expectiles, Expectile Depth and Multiple-Output Expectile Regression," TSE Working Papers 19-1022, Toulouse School of Economics (TSE), revised Feb 2023.
    7. Laurent Gardes & Stéphane Girard, 2021. "On the estimation of the variability in the distribution tail," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 30(4), pages 884-907, December.
    8. Girard, Stéphane & Stupfler, Gilles & Usseglio-Carleve, Antoine, 2022. "Functional estimation of extreme conditional expectiles," Econometrics and Statistics, Elsevier, vol. 21(C), pages 131-158.
    9. Bernardi, Mauro & Bignozzi, Valeria & Petrella, Lea, 2017. "On the Lp-quantiles for the Student t distribution," Statistics & Probability Letters, Elsevier, vol. 128(C), pages 77-83.
    10. Bellini, Fabio & Klar, Bernhard & Müller, Alfred & Rosazza Gianin, Emanuela, 2014. "Generalized quantiles as risk measures," Insurance: Mathematics and Economics, Elsevier, vol. 54(C), pages 41-48.
    11. Arab, Idir & Lando, Tommaso & Oliveira, Paulo Eduardo, 2022. "Comparison of Lp-quantiles and related skewness measures," Statistics & Probability Letters, Elsevier, vol. 183(C).
    12. Stéphane Girard & Gilles Stupfler & Antoine Usseglio‐Carleve, 2022. "Nonparametric extreme conditional expectile estimation," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 49(1), pages 78-115, March.
    13. Silvana M. Pesenti & Steven Vanduffel, 2023. "Optimal Transport Divergences induced by Scoring Functions," Papers 2311.12183, arXiv.org, revised Apr 2024.
    14. Collin Philipps, 2022. "Interpreting Expectiles," Working Papers 2022-01, Department of Economics and Geosciences, US Air Force Academy.
    15. Valeria Bignozzi & Luca Merlo & Lea Petrella, 2022. "Inter-order relations between moments of a Student $t$ distribution, with an application to $L_p$-quantiles," Papers 2209.12855, arXiv.org.
    16. Bellini, Fabio & Rosazza Gianin, Emanuela, 2012. "Haezendonck–Goovaerts risk measures and Orlicz quantiles," Insurance: Mathematics and Economics, Elsevier, vol. 51(1), pages 107-114.

    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. Peracchi, Franco, 2002. "On estimating conditional quantiles and distribution functions," Computational Statistics & Data Analysis, Elsevier, vol. 38(4), pages 433-447, February.
    2. Halkos, George E., 2011. "Nonparametric modelling of biodiversity: Determinants of threatened species," Journal of Policy Modeling, Elsevier, vol. 33(4), pages 618-635, July.
    3. de Bondt, Gabe & Peltonen, Tuomas A. & Santabárbara, Daniel, 2010. "Booms and busts in China's stock market: Estimates based on fundamentals," Working Paper Series 1190, European Central Bank.
    4. Halkos, George, 2010. "Modelling biodiversity," MPRA Paper 39075, University Library of Munich, Germany.
    5. Kollias Christos & Paleologou Suzanna-Maria & Tzeremes Panayiotis, 2020. "Defence Spending and Unemployment in the USA: Disaggregated Analysis by Gender and Age Groups," Peace Economics, Peace Science, and Public Policy, De Gruyter, vol. 26(2), pages 1-13, May.
    6. Insik Min & Inchul Kim, 2004. "A Monte Carlo comparison of parametric and nonparametric quantile regressions," Applied Economics Letters, Taylor & Francis Journals, vol. 11(2), pages 71-74.
    7. Gaglianone, Wagner Piazza & Guillén, Osmani Teixeira de Carvalho & Figueiredo, Francisco Marcos Rodrigues, 2018. "Estimating inflation persistence by quantile autoregression with quantile-specific unit roots," Economic Modelling, Elsevier, vol. 73(C), pages 407-430.
    8. Mohammedi, Mustapha & Bouzebda, Salim & Laksaci, Ali, 2021. "The consistency and asymptotic normality of the kernel type expectile regression estimator for functional data," Journal of Multivariate Analysis, Elsevier, vol. 181(C).
    9. Marilena FURNO & Francesco CARACCIOLO, 2017. "Beyond the mean: Estimating consumer demand systems in the tails," Agricultural Economics, Czech Academy of Agricultural Sciences, vol. 63(10), pages 449-460.
    10. Sánchez Serrano, Antonio, 2021. "The impact of non-performing loans on bank lending in Europe: An empirical analysis," The North American Journal of Economics and Finance, Elsevier, vol. 55(C).
    11. Swamy, Vighneswara & Dharani, M. & Takeda, Fumiko, 2019. "Investor attention and Google Search Volume Index: Evidence from an emerging market using quantile regression analysis," Research in International Business and Finance, Elsevier, vol. 50(C), pages 1-17.
    12. Machado, Jose A. F. & Silva, J. M. C. Santos, 2000. "Glejser's test revisited," Journal of Econometrics, Elsevier, vol. 97(1), pages 189-202, July.
    13. Moshe Buchinsky, 1998. "Recent Advances in Quantile Regression Models: A Practical Guideline for Empirical Research," Journal of Human Resources, University of Wisconsin Press, vol. 33(1), pages 88-126.
    14. Naifar, Nader & Hammoudeh, Shawkat, 2016. "Do global financial distress and uncertainties impact GCC and global sukuk return dynamics?," Pacific-Basin Finance Journal, Elsevier, vol. 39(C), pages 57-69.
    15. Vighneswara Swamy & M. Dharani, 2020. "RETRACTED ARTICLE: Google Search Intensity and the Investor Attention Effect: A Quantile Regression Approach," Journal of Quantitative Economics, Springer;The Indian Econometric Society (TIES), vol. 18(2), pages 403-423, June.
    16. Yingying Jiang & Fuming Lin & Yong Zhou, 2021. "The kth power expectile regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(1), pages 83-113, February.
    17. Gregory Kordas, 2006. "Smoothed binary regression quantiles," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 21(3), pages 387-407, April.
    18. Yang, Ann Shawing, 2016. "Calendar trading of Taiwan stock market: A study of holidays on trading detachment and interruptions," Emerging Markets Review, Elsevier, vol. 28(C), pages 140-154.
    19. Buchinsky, Moshe, 1995. "Quantile regression, Box-Cox transformation model, and the U.S. wage structure, 1963-1987," Journal of Econometrics, Elsevier, vol. 65(1), pages 109-154, January.
    20. Hasan, Md. Bokhtiar & Kabir Hassan, M. & Gider, Zeynullah & Tahsin Rafia, Humaira & Rashid, Mamunur, 2023. "Searching hedging instruments against diverse global risks and uncertainties," The North American Journal of Economics and Finance, Elsevier, vol. 66(C).

    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:29:y:1996:i:2:p:107-115. 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.