IDEAS home Printed from https://ideas.repec.org/a/eee/jmvana/v101y2010i4p811-823.html
   My bibliography  Save this article

Residual variance estimation using a nearest neighbor statistic

Author

Listed:
  • Liitiäinen, Elia
  • Corona, Francesco
  • Lendasse, Amaury

Abstract

In this paper we consider the problem of estimating E[(Y-E[Y|X])2] based on a finite sample of independent, but not necessarily identically distributed, random variables . We analyze the theoretical properties of a recently developed estimator. It is shown that the estimator has many theoretically interesting properties, while the practical implementation is simple.

Suggested Citation

  • Liitiäinen, Elia & Corona, Francesco & Lendasse, Amaury, 2010. "Residual variance estimation using a nearest neighbor statistic," Journal of Multivariate Analysis, Elsevier, vol. 101(4), pages 811-823, April.
    • Handle: RePEc:eee:jmvana:v:101:y:2010:i:4:p:811-823
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0047-259X(10)00003-5
    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. Tong, Howell & Yao, Qiwei, 2000. "Nonparametric estimation of ratios of noise to signal in stochastic regression," LSE Research Online Documents on Economics 6324, London School of Economics and Political Science, LSE Library.
    2. Cai, T. Tony & Levine, Michael & Wang, Lie, 2009. "Variance function estimation in multivariate nonparametric regression with fixed design," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 126-136, January.
    3. Tiejun Tong & Yuedong Wang, 2005. "Estimating residual variance in nonparametric regression using least squares," Biometrika, Biometrika Trust, vol. 92(4), pages 821-830, December.
    4. Axel Munk & Nicolai Bissantz & Thorsten Wagner & Gudrun Freitag, 2005. "On difference‐based variance estimation in nonparametric regression when the covariate is high dimensional," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 67(1), pages 19-41, February.
    5. Kohler, Michael & Krzyzak, Adam & Walk, Harro, 2006. "Rates of convergence for partitioning and nearest neighbor regression estimates with unbounded data," Journal of Multivariate Analysis, Elsevier, vol. 97(2), pages 311-323, February.
    6. Devroye Luc & Schäfer Dominik & Györfi László & Walk Harro, 2003. "The estimation problem of minimum mean squared error," Statistics & Risk Modeling, De Gruyter, vol. 21(1), pages 15-28, January.
    7. Spokoiny, Vladimir, 2002. "Variance Estimation for High-Dimensional Regression Models," Journal of Multivariate Analysis, Elsevier, vol. 82(1), pages 111-133, July.
    8. Fan, Jianqing & Yao, Qiwei, 1998. "Efficient estimation of conditional variance functions in stochastic regression," LSE Research Online Documents on Economics 6635, London School of Economics and Political Science, LSE Library.
    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. Györfi László & Walk Harro, 2013. "Rate of convergence of the density estimation of regression residual," Statistics & Risk Modeling, De Gruyter, vol. 30(1), pages 55-74, March.
    2. Paola Gloria Ferrario, 2018. "Partitioning estimation of local variance based on nearest neighbors under censoring," Statistical Papers, Springer, vol. 59(2), pages 423-447, June.
    3. Kohler, Michael & Krzyżak, Adam, 2013. "Optimal global rates of convergence for interpolation problems with random design," Statistics & Probability Letters, Elsevier, vol. 83(8), pages 1871-1879.
    4. P. G. Ferrario & H. Walk, 2012. "Nonparametric partitioning estimation of residual and local variance based on first and second nearest neighbours," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 1019-1039, December.

    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. P. G. Ferrario & H. Walk, 2012. "Nonparametric partitioning estimation of residual and local variance based on first and second nearest neighbours," Journal of Nonparametric Statistics, Taylor & Francis Journals, vol. 24(4), pages 1019-1039, December.
    2. Peter Hall & Joel L. Horowitz, 2013. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers 29/13, Institute for Fiscal Studies.
    3. Peter Hall & Joel L. Horowitz, 2012. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers 14/12, Institute for Fiscal Studies.
    4. Paola Gloria Ferrario, 2018. "Partitioning estimation of local variance based on nearest neighbors under censoring," Statistical Papers, Springer, vol. 59(2), pages 423-447, June.
    5. Jingxin Zhao & Heng Peng & Tao Huang, 2018. "Variance estimation for semiparametric regression models by local averaging," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 27(2), pages 453-476, June.
    6. Hall, Peter & Yatchew, Adonis, 2010. "Nonparametric least squares estimation in derivative families," Journal of Econometrics, Elsevier, vol. 157(2), pages 362-374, August.
    7. Peter Hall & Joel L. Horowitz, 2012. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers CWP14/12, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    8. Peter Hall & Joel L. Horowitz, 2013. "A simple bootstrap method for constructing nonparametric confidence bands for functions," CeMMAP working papers CWP29/13, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    9. Wang, WenWu & Yu, Ping, 2017. "Asymptotically optimal differenced estimators of error variance in nonparametric regression," Computational Statistics & Data Analysis, Elsevier, vol. 105(C), pages 125-143.
    10. 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.
    11. Mendez, Guillermo & Lohr, Sharon, 2011. "Estimating residual variance in random forest regression," Computational Statistics & Data Analysis, Elsevier, vol. 55(11), pages 2937-2950, November.
    12. Levine, Michael, 2015. "Minimax rate of convergence for an estimator of the functional component in a semiparametric multivariate partially linear model," Journal of Multivariate Analysis, Elsevier, vol. 140(C), pages 283-290.
    13. Juhyun Park & Burkhardt Seifert, 2010. "Local additive estimation," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 72(2), pages 171-191, March.
    14. Cai, T. Tony & Levine, Michael & Wang, Lie, 2009. "Variance function estimation in multivariate nonparametric regression with fixed design," Journal of Multivariate Analysis, Elsevier, vol. 100(1), pages 126-136, January.
    15. Müller, Hans-Georg & Sen, Rituparna & Stadtmüller, Ulrich, 2011. "Functional data analysis for volatility," Journal of Econometrics, Elsevier, vol. 165(2), pages 233-245.
    16. Dette, Holger & Wieczorek, Gabriele, 2007. "Testing for a constant coefficient of variation in nonparametric regression," Technical Reports 2007,36, Technische Universität Dortmund, Sonderforschungsbereich 475: Komplexitätsreduktion in multivariaten Datenstrukturen.
    17. WenWu Wang & Lu Lin & Li Yu, 2017. "Optimal variance estimation based on lagged second-order difference in nonparametric regression," Computational Statistics, Springer, vol. 32(3), pages 1047-1063, September.
    18. Inder Tecuapetla-Gómez & Axel Munk, 2017. "Autocovariance Estimation in Regression with a Discontinuous Signal and m-Dependent Errors: A Difference-Based Approach," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 44(2), pages 346-368, June.
    19. Eckhard Liebscher, 2012. "Model checks for parametric regression models," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 21(1), pages 132-155, March.
    20. 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.

    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:jmvana:v:101:y:2010:i:4:p:811-823. 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.