IDEAS home Printed from https://ideas.repec.org/a/eee/csdana/v189y2024ics0167947323001627.html
   My bibliography  Save this article

Testing the parametric form of the conditional variance in regressions based on distance covariance

Author

Listed:
  • Hu, Yue
  • Li, Haiqi
  • Tan, Falong

Abstract

A new test based on distance covariance is proposed for testing the parametric form of the conditional variance in parametric and nonparametric regression models. Inherit from the nice properties of distance covariance, the new test is very easy to implement in practice and less effected by the dimensionality of covariates. The asymptotic properties of the test statistic are investigated under the null and alternative hypotheses. The proposed test is consistent against any alternative hypothesis and can detect some classes of local alternative hypotheses converging to the null hypothesis at the parametric rate in both the parametric and nonparametric settings. As the limiting null distribution of the test statistic is intractable, a smooth residual bootstrap is proposed to approximate the limiting null distribution. Simulation studies are conducted to assess the finite sample performance of the proposed test. A real data set is also analyzed for illustration.

Suggested Citation

  • Hu, Yue & Li, Haiqi & Tan, Falong, 2024. "Testing the parametric form of the conditional variance in regressions based on distance covariance," Computational Statistics & Data Analysis, Elsevier, vol. 189(C).
    • Handle: RePEc:eee:csdana:v:189:y:2024:i:c:s0167947323001627
    DOI: 10.1016/j.csda.2023.107851
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0167947323001627
    Download Restriction: Full text for ScienceDirect subscribers only.
    File URL: https://libkey.io/10.1016/j.csda.2023.107851?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 search for a different version of it.

    References listed on IDEAS

    as
    1. H. Dette & A. Munk, 1998. "Testing heteroscedasticity in nonparametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 60(4), pages 693-708.
    2. A. Sen & B. Sen, 2014. "Testing independence and goodness-of-fit in linear models," Biometrika, Biometrika Trust, vol. 101(4), pages 927-942.
    3. Holger Dette & Natalie Neumeyer & Ingrid Van Keilegom, 2007. "A new test for the parametric form of the variance function in non‐parametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 903-917, November.
    4. Su, Liangjun & Ullah, Aman, 2013. "A Nonparametric Goodness-Of-Fit-Based Test For Conditional Heteroskedasticity," Econometric Theory, Cambridge University Press, vol. 29(1), pages 187-212, February.
    5. Breusch, T S & Pagan, A R, 1979. "A Simple Test for Heteroscedasticity and Random Coefficient Variation," Econometrica, Econometric Society, vol. 47(5), pages 1287-1294, September.
    6. Lan Wang & Xiao-Hua Zhou, 2007. "Assessing the Adequacy of Variance Function in Heteroscedastic Regression Models," Biometrics, The International Biometric Society, vol. 63(4), pages 1218-1225, December.
    7. Samarakoon, Nishantha & Song, Weixing, 2011. "Minimum distance conditional variance function checking in heteroscedastic regression models," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 579-600, March.
    8. Natalie Neumeyer, 2009. "Smooth Residual Bootstrap for Empirical Processes of Non‐parametric Regression Residuals," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 204-228, June.
    Full references (including those not matched with items on IDEAS)

    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. Samarakoon, Nishantha & Song, Weixing, 2011. "Minimum distance conditional variance function checking in heteroscedastic regression models," Journal of Multivariate Analysis, Elsevier, vol. 102(3), pages 579-600, March.
    2. Li, Zhaoyuan & Yao, Jianfeng, 2019. "Testing for heteroscedasticity in high-dimensional regressions," Econometrics and Statistics, Elsevier, vol. 9(C), pages 122-139.
    3. Juan Carlos Pardo-Fernández & M. Dolores Jiménez-Gamero, 2019. "A model specification test for the variance function in nonparametric regression," AStA Advances in Statistical Analysis, Springer;German Statistical Society, vol. 103(3), pages 387-410, September.
    4. Feve, Frederique & Florens, Jean-Pierre & Van Keilegom, Ingrid, 2012. "Estimation of conditional ranks and tests of exogeneity in nonparametric nonseparable models," LIDAM Discussion Papers ISBA 2012036, Université catholique de Louvain, Institute of Statistics, Biostatistics and Actuarial Sciences (ISBA).
    5. Holger Dette & Juan Carlos Pardo‐Fernández & Ingrid Van Keilegom, 2009. "Goodness‐of‐Fit Tests for Multiplicative Models with Dependent Data," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(4), pages 782-799, December.
    6. Holger Dette & Natalie Neumeyer & Ingrid Van Keilegom, 2007. "A new test for the parametric form of the variance function in non‐parametric regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 69(5), pages 903-917, November.
    7. Fan, Caiyun & Lu, Wenbin & Zhou, Yong, 2021. "Testing error heterogeneity in censored linear regression," Computational Statistics & Data Analysis, Elsevier, vol. 161(C).
    8. Jun Zhang & Zhenghui Feng & Xiaoguang Wang, 2018. "A constructive hypothesis test for the single-index models with two groups," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 70(5), pages 1077-1114, October.
    9. Jana Jurečková & Radim Navrátil, 2014. "Rank tests in heteroscedastic linear model with nuisance parameters," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 77(3), pages 433-450, April.
    10. Neumeyer, Natalie & Van Keilegom, Ingrid, 2010. "Estimating the error distribution in nonparametric multiple regression with applications to model testing," Journal of Multivariate Analysis, Elsevier, vol. 101(5), pages 1067-1078, May.
    11. Florens, Jean-Pierre & Simar, Léopold & Van Keilegom, Ingrid, 2014. "Frontier estimation in nonparametric location-scale models," Journal of Econometrics, Elsevier, vol. 178(P3), pages 456-470.
    12. Heuchenne, Cédric & Van Keilegom, Ingrid, 2010. "Goodness-of-fit tests for the error distribution in nonparametric regression," Computational Statistics & Data Analysis, Elsevier, vol. 54(8), pages 1942-1951, August.
    13. Zhu, Xuehu & Guo, Xu & Lin, Lu & Zhu, Lixing, 2015. "Heteroscedasticity checks for single index models," Journal of Multivariate Analysis, Elsevier, vol. 136(C), pages 41-55.
    14. Wenceslao González-Manteiga & Rosa Crujeiras, 2013. "An updated review of Goodness-of-Fit tests for regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(3), pages 361-411, September.
    15. Mario Francisco-Fernández & Juan Vilar-Fernández, 2009. "Two tests for heteroscedasticity in nonparametric regression," Computational Statistics, Springer, vol. 24(1), pages 145-163, February.
    16. Zhu, Xuehu & Chen, Fei & Guo, Xu & Zhu, Lixing, 2016. "Heteroscedasticity testing for regression models: A dimension reduction-based model adaptive approach," Computational Statistics & Data Analysis, Elsevier, vol. 103(C), pages 263-283.
    17. You, Jinhong & Chen, Gemai, 2005. "Testing heteroscedasticity in partially linear regression models," Statistics & Probability Letters, Elsevier, vol. 73(1), pages 61-70, June.
    18. Zhidong Bai & Guangming Pan & Yanqing Yin, 2018. "A central limit theorem for sums of functions of residuals in a high-dimensional regression model with an application to variance homoscedasticity test," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(4), pages 896-920, December.
    19. Dette, Holger & Hetzler, Benjamin, 2008. "A martingale-transform goodness-of-fit test for the form of the conditional variance," Technical Reports 2008,07, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    20. Estate V. Khmaladze, 2021. "Distribution-free testing in linear and parametric regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 73(6), pages 1063-1087, December.

    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:csdana:v:189:y:2024:i:c:s0167947323001627. 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/locate/csda .

    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.