IDEAS home Printed from https://ideas.repec.org/p/msh/ebswps/2006-8.html
   My bibliography  Save this paper

Local Linear Multivariate Regression with Variable Bandwidth in the Presence of Heteroscedasticity

Author

Listed:
  • Azhong Ye
  • Rob J Hyndman
  • Zinai Li

Abstract

We present a local linear estimator with variable bandwidth for multivariate nonparametric regression. We prove its consistency and asymptotic normality in the interior of the observed data and obtain its rates of convergence. This result is used to obtain practical direct plug-in bandwidth selectors for heteroscedastic regression in one and two dimensions. We show that the local linear estimator with variable bandwidth has better goodness-of-fit properties than the local linear estimator with constant bandwidth, in the presence of heteroscedasticity.

Suggested Citation

  • Azhong Ye & Rob J Hyndman & Zinai Li, 2006. "Local Linear Multivariate Regression with Variable Bandwidth in the Presence of Heteroscedasticity," Monash Econometrics and Business Statistics Working Papers 8/06, Monash University, Department of Econometrics and Business Statistics.
    • Handle: RePEc:msh:ebswps:2006-8
    as

    Download full text from publisher

    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2006/wp8-06.pdf
    Download Restriction: no
    ---><---

    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. Adonis Yatchew, 1998. "Nonparametric Regression Techniques in Economics," Journal of Economic Literature, American Economic Association, vol. 36(2), pages 669-721, June.
    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. Shim, Jooyong & Hwang, Changha, 2009. "Support vector censored quantile regression under random censoring," Computational Statistics & Data Analysis, Elsevier, vol. 53(4), pages 912-919, February.
    2. Jooyong Shim & Changha Hwang & Kyungha Seok, 2014. "Composite support vector quantile regression estimation," Computational Statistics, Springer, vol. 29(6), pages 1651-1665, December.
    3. Jungwoo Kim & Joocheol Kim, 2017. "Nonparametric forecasting with one-sided kernel adopting pseudo one-step ahead data," Working papers 2017rwp-102, Yonsei University, Yonsei Economics Research Institute.

    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. Corak, Miles & Lauzon, Darren, 2009. "Differences in the distribution of high school achievement: The role of class-size and time-in-term," Economics of Education Review, Elsevier, vol. 28(2), pages 189-198, April.
    2. Ichimura, Hidehiko & Todd, Petra E., 2007. "Implementing Nonparametric and Semiparametric Estimators," Handbook of Econometrics, in: J.J. Heckman & E.E. Leamer (ed.), Handbook of Econometrics, edition 1, volume 6, chapter 74, Elsevier.
    3. Koop, Gary & Poirier, Dale J., 2004. "Bayesian variants of some classical semiparametric regression techniques," Journal of Econometrics, Elsevier, vol. 123(2), pages 259-282, December.
    4. Long Feng & Changliang Zou & Zhaojun Wang & Lixing Zhu, 2015. "Robust comparison of regression curves," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 24(1), pages 185-204, March.
    5. Temel, Tugrul T., 2001. "A Nonparametric Hypothesis Test Via The Bootstrap Resampling," 2001 Annual meeting, August 5-8, Chicago, IL 20600, American Agricultural Economics Association (New Name 2008: Agricultural and Applied Economics Association).
    6. Holger Dette & Kay Pilz, 2009. "On the estimation of a monotone conditional variance in nonparametric regression," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 61(1), pages 111-141, March.
    7. Alberto Abadie & Guido W. Imbens, 2002. "Simple and Bias-Corrected Matching Estimators for Average Treatment Effects," NBER Technical Working Papers 0283, National Bureau of Economic Research, Inc.
    8. Subal Kumbhakar & Efthymios Tsionas, 2008. "Scale and efficiency measurement using a semiparametric stochastic frontier model: evidence from the U.S. commercial banks," Empirical Economics, Springer, vol. 34(3), pages 585-602, June.
    9. Nuria Gallego & Carlos Llano, 2014. "The Border Effect and the Nonlinear Relationship between Trade and Distance," Review of International Economics, Wiley Blackwell, vol. 22(5), pages 1016-1048, November.
    10. Chamon, Marcos & Schumacher, Julian & Trebesch, Christoph, 2018. "Foreign-Law Bonds: Can They Reduce Sovereign Borrowing Costs?," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 114, pages 164-179.
    11. Malcolm Keswell, 2004. "Non‐Linear Earnings Dynamics In Post‐Apartheid South Africa," South African Journal of Economics, Economic Society of South Africa, vol. 72(5), pages 913-939, December.
    12. Vincenzo Verardi, 2013. "Semiparametric regression in Stata," United Kingdom Stata Users' Group Meetings 2013 14, Stata Users Group.
    13. Fernández-Huertas Moraga, Jesús, 2013. "Understanding different migrant selection patterns in rural and urban Mexico," Journal of Development Economics, Elsevier, vol. 103(C), pages 182-201.
    14. Camelia Minoiu & Sanjay Reddy, 2014. "Kernel density estimation on grouped data: the case of poverty assessment," The Journal of Economic Inequality, Springer;Society for the Study of Economic Inequality, vol. 12(2), pages 163-189, June.
    15. Lv, Zhike, 2017. "Intelligence and corruption: An empirical investigation in a non-linear framework," Journal of Behavioral and Experimental Economics (formerly The Journal of Socio-Economics), Elsevier, vol. 69(C), pages 83-91.
    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. Ghodeswar, Archana & Oliver, Matthew E., 2022. "Trading one waste for another? Unintended consequences of fly ash reuse in the Indian electric power sector," Energy Policy, Elsevier, vol. 165(C).
    18. Soderbom, Mans & Teal, Francis, 2004. "Size and efficiency in African manufacturing firms: evidence from firm-level panel data," Journal of Development Economics, Elsevier, vol. 73(1), pages 369-394, February.
    19. Holger Dette & Mareen Marchlewski & Jens Wagener, 2012. "Testing for a constant coefficient of variation in nonparametric regression by empirical processes," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 64(5), pages 1045-1070, October.
    20. Cowan, Robin & Jonard, Nicolas & Zimmermann, J-B, 2004. "Networks as Emergent Structures from Bilateral Collaboration," Research Memorandum 017, Maastricht University, Maastricht Economic Research Institute on Innovation and Technology (MERIT).

    More about this item

    Keywords

    Heteroscedasticity; kernel smoothing; local linear regression; plug-in bandwidth; variable bandwidth.;
    All these keywords.

    JEL classification:

    • C12 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Hypothesis Testing: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:msh:ebswps:2006-8. 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: Professor Xibin Zhang (email available below). General contact details of provider: https://edirc.repec.org/data/dxmonau.html .

    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.