IDEAS home Printed from https://ideas.repec.org/a/taf/japsta/v42y2015i11p2432-2448.html
   My bibliography  Save this article

Heteroscedasticity diagnostics in varying-coefficient partially linear regression models and applications in analyzing Boston housing data

Author

Listed:
  • Jin-Guan Lin
  • Yan-Yong Zhao
  • Hong-Xia Wang

Abstract

It is important to detect the variance heterogeneity in regression model because efficient inference requires that heteroscedasticity is taken into consideration if it really exists. For the varying-coefficient partially linear regression models, however, the problem of detecting heteroscedasticity has received very little attention. In this paper, we present two classes of tests of heteroscedasticity for varying-coefficient partially linear regression models. The first test statistic is constructed based on the residuals, in which the error term is from a normal distribution. The second one is motivated by the idea that testing heteroscedasticity is equivalent to testing pseudo-residuals for a constant mean. Asymptotic normality is established with different rates corresponding to the null hypothesis of homoscedasticity and the alternative. Some Monte Carlo simulations are conducted to investigate the finite sample performance of the proposed tests. The test methodologies are illustrated with a real data set example.

Suggested Citation

  • Jin-Guan Lin & Yan-Yong Zhao & Hong-Xia Wang, 2015. "Heteroscedasticity diagnostics in varying-coefficient partially linear regression models and applications in analyzing Boston housing data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 42(11), pages 2432-2448, November.
    • Handle: RePEc:taf:japsta:v:42:y:2015:i:11:p:2432-2448
    DOI: 10.1080/02664763.2015.1043623
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/10.1080/02664763.2015.1043623
    Download Restriction: Access to full text is restricted to subscribers.
    File URL: https://libkey.io/10.1080/02664763.2015.1043623?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. Manuel Galea & Gilberto Paula & Miguel Uribe-Opazo, 2003. "On influence diagnostic in univariate elliptical linear regression models," Statistical Papers, Springer, vol. 44(1), pages 23-45, January.
    2. Bo-Cheng Wei & Jian-Qing Shi & Wing-Kam Fung & Yue-Qing Hu, 1998. "Testing for Varying Dispersion in Exponential Family Nonlinear Models," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 50(2), pages 277-294, June.
    3. Paula, Gilberto A. & Medeiros, Marcio & Vilca-Labra, Filidor E., 2009. "Influence diagnostics for linear models with first-order autoregressive elliptical errors," Statistics & Probability Letters, Elsevier, vol. 79(3), pages 339-346, February.
    4. Huang, Zhensheng & Zhang, Riquan, 2009. "Empirical likelihood for nonparametric parts in semiparametric varying-coefficient partially linear models," Statistics & Probability Letters, Elsevier, vol. 79(16), pages 1798-1808, August.
    5. Cysneiros, Francisco José A. & Paula, Gilberto A. & Galea, Manuel, 2007. "Heteroscedastic symmetrical linear models," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1084-1090, June.
    6. Weihua Zhao & Riquan Zhang & Jicai Liu, 2013. "Robust variable selection for the varying coefficient model based on composite L 1 -- L 2 regression," Journal of Applied Statistics, Taylor & Francis Journals, vol. 40(9), pages 2024-2040, September.
    7. Galea, Manuel & Paula, Gilberto A. & Cysneiros, Francisco José A., 2005. "On diagnostics in symmetrical nonlinear models," Statistics & Probability Letters, Elsevier, vol. 73(4), pages 459-467, July.
    8. Harrison, David Jr. & Rubinfeld, Daniel L., 1978. "Hedonic housing prices and the demand for clean air," Journal of Environmental Economics and Management, Elsevier, vol. 5(1), pages 81-102, March.
    9. Yingcun Xia, 2004. "Efficient estimation for semivarying-coefficient models," Biometrika, Biometrika Trust, vol. 91(3), pages 661-681, September.
    10. John Xu Zheng, 1996. "A consistent test of functional form via nonparametric estimation techniques," Journal of Econometrics, Elsevier, vol. 75(2), pages 263-289, December.
    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. Chun-Zheng Cao & Jin-Guan Lin & Li-Xing Zhu, 2010. "Heteroscedasticity and/or autocorrelation diagnostics in nonlinear models with AR(1) and symmetrical errors," Statistical Papers, Springer, vol. 51(4), pages 813-836, December.
    2. Carlos Eduardo M. Relvas & Gilberto A. Paula, 2016. "Partially linear models with first-order autoregressive symmetric errors," Statistical Papers, Springer, vol. 57(3), pages 795-825, September.
    3. Ibacache-Pulgar, Germán & Paula, Gilberto A., 2011. "Local influence for Student-t partially linear models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1462-1478, March.
    4. Alcantara, Izabel Cristina & Cysneiros, Francisco José A., 2013. "Linear regression models with slash-elliptical errors," Computational Statistics & Data Analysis, Elsevier, vol. 64(C), pages 153-164.
    5. Villegas, Cristian & Paula, Gilberto A. & Cysneiros, Francisco José A. & Galea, Manuel, 2013. "Influence diagnostics in generalized symmetric linear models," Computational Statistics & Data Analysis, Elsevier, vol. 59(C), pages 161-170.
    6. Germán Ibacache-Pulgar & Gilberto Paula & Francisco Cysneiros, 2013. "Semiparametric additive models under symmetric distributions," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 22(1), pages 103-121, March.
    7. Sanying Feng & Liugen Xue, 2014. "Bias-corrected statistical inference for partially linear varying coefficient errors-in-variables models with restricted condition," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 66(1), pages 121-140, February.
    8. Fang Lu & Jing Yang & Xuewen Lu, 2022. "One-step oracle procedure for semi-parametric spatial autoregressive model and its empirical application to Boston housing price data," Empirical Economics, Springer, vol. 62(6), pages 2645-2671, June.
    9. Joelmir A. Borssoi & Gilberto A. Paula & Manuel Galea, 2020. "Elliptical linear mixed models with a covariate subject to measurement error," Statistical Papers, Springer, vol. 61(1), pages 31-69, February.
    10. Jin-Guan Lin & Li-Xing Zhu & Feng-Chang Xie, 2009. "Heteroscedasticity diagnostics for t linear regression models," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 70(1), pages 59-77, June.
    11. Cysneiros, Francisco José A. & Paula, Gilberto A. & Galea, Manuel, 2007. "Heteroscedastic symmetrical linear models," Statistics & Probability Letters, Elsevier, vol. 77(11), pages 1084-1090, June.
    12. Malikov, Emir & Sun, Yiguo, 2017. "Semiparametric estimation and testing of smooth coefficient spatial autoregressive models," Journal of Econometrics, Elsevier, vol. 199(1), pages 12-34.
    13. Li, Ai-Ping & Chen, Zhao-Xia & Xie, Feng-Chang, 2012. "Diagnostic analysis for heterogeneous log-Birnbaum–Saunders regression models," Statistics & Probability Letters, Elsevier, vol. 82(9), pages 1690-1698.
    14. Cibele M. Russo & Gilberto A. Paula & Francisco Jos� A. Cysneiros & Reiko Aoki, 2012. "Influence diagnostics in heteroscedastic and/or autoregressive nonlinear elliptical models for correlated data," Journal of Applied Statistics, Taylor & Francis Journals, vol. 39(5), pages 1049-1067, October.
    15. Zhou, Ling & Lin, Huazhen & Chen, Kani & Liang, Hua, 2019. "Efficient estimation and computation of parameters and nonparametric functions in generalized semi/non-parametric regression models," Journal of Econometrics, Elsevier, vol. 213(2), pages 593-607.
    16. Jin-Guan Lin & Li-Xing Zhu & Chun-Zheng Cao & Yong Li, 2011. "Tests of heteroscedasticity and correlation in multivariate t regression models with AR and ARMA errors," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(7), pages 1509-1531, August.
    17. Zhao, Yan-Yong & Lin, Jin-Guan & Xu, Pei-Rong & Ye, Xu-Guo, 2015. "Orthogonality-projection-based estimation for semi-varying coefficient models with heteroscedastic errors," Computational Statistics & Data Analysis, Elsevier, vol. 89(C), pages 204-221.
    18. Artur J. Lemonte & Alexandre G. Patriota, 2011. "Influence diagnostics in Birnbaum--Saunders nonlinear regression models," Journal of Applied Statistics, Taylor & Francis Journals, vol. 38(5), pages 871-884, February.
    19. Francisco J. A. Cysneiros & Víctor Leiva & Shuangzhe Liu & Carolina Marchant & Paulo Scalco, 2019. "A Cobb–Douglas type model with stochastic restrictions: formulation, local influence diagnostics and data analytics in economics," Quality & Quantity: International Journal of Methodology, Springer, vol. 53(4), pages 1693-1719, July.
    20. Xie, Chuanlong & Zhu, Lixing, 2019. "A goodness-of-fit test for variable-adjusted models," Computational Statistics & Data Analysis, Elsevier, vol. 138(C), pages 27-48.

    More about this item

    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:taf:japsta:v:42:y:2015:i:11:p:2432-2448. 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: Chris Longhurst (email available below). General contact details of provider: http://www.tandfonline.com/CJAS20 .

    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.