IDEAS home Printed from https://ideas.repec.org/p/zbw/sfb373/199799.html
   My bibliography  Save this paper

Multivariate plug-in bandwidth for local linear regression

Author

Listed:
  • Yang, Lijian
  • Tschernig, Rolf

Abstract

Optimal bandwidths for local polynomial regression usually involve functionals of the derivatives of the unknown regression function. In the multivariate case, estimates of these functionals are not readily available, primarily because estimating multivariate derivatives is complicated. In this paper, an estimator of multivariate second derivative is obtained via local quadratic regression with cross terms left out. This estimator has the optimal rate of convergence but is simpler and uses a lot less computing time than the full local quadratic estimator. Using this as a pilot estimator, an estimator of the integrated squared Laplacian of a multivariate regression function is obtained which leads to a plug-in formula of the optimal bandwidth for multivariate local linear regression. This bandwidth has good theoretical properties as well as satisfactory performance in our simulation study. It is also recommended for variable selection methods.

Suggested Citation

  • Yang, Lijian & Tschernig, Rolf, 1997. "Multivariate plug-in bandwidth for local linear regression," SFB 373 Discussion Papers 1997,99, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:199799
    as

    Download full text from publisher

    File URL: https://www.econstor.eu/bitstream/10419/66265/1/729733696.pdf
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Rolf Tschernig & Lijian Yang, 2000. "Nonparametric Lag Selection for Time Series," Journal of Time Series Analysis, Wiley Blackwell, vol. 21(4), pages 457-487, July.
    2. Hall, Peter, 1984. "Central limit theorem for integrated square error of multivariate nonparametric density estimators," Journal of Multivariate Analysis, Elsevier, vol. 14(1), pages 1-16, February.
    3. Härdle, Wolfgang & Tsybakov, A. & Yang, L., 1996. "Nonparametric Vector Autoregression," SFB 373 Discussion Papers 1996,61, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    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. Rolf Tschernig & Lijian Yang, 2000. "Nonparametric Estimation of Generalized Impulse Response Functions," Econometric Society World Congress 2000 Contributed Papers 1417, Econometric Society.
    2. Lijian Yang & Wolfgang Hardle & Jens Nielsen, 1999. "Nonparametric Autoregression with Multiplicative Volatility and Additive mean," Journal of Time Series Analysis, Wiley Blackwell, vol. 20(5), pages 579-604, September.
    3. Mohamed Chikhi & Claude Diebolt, 2010. "Nonparametric analysis of financial time series by the Kernel methodology," Quality & Quantity: International Journal of Methodology, Springer, vol. 44(5), pages 865-880, August.
    4. Marcelo Fernandes & Breno Neri, 2010. "Nonparametric Entropy-Based Tests of Independence Between Stochastic Processes," Econometric Reviews, Taylor & Francis Journals, vol. 29(3), pages 276-306.
    5. Su, Liangjun, 2006. "A simple test for multivariate conditional symmetry," Economics Letters, Elsevier, vol. 93(3), pages 374-378, December.
    6. Whitney K. Newey & Frank Windmeijer, 2005. "GMM with many weak moment conditions," CeMMAP working papers CWP18/05, Centre for Microdata Methods and Practice, Institute for Fiscal Studies.
    7. Ouimet, Frédéric & Tolosana-Delgado, Raimon, 2022. "Asymptotic properties of Dirichlet kernel density estimators," Journal of Multivariate Analysis, Elsevier, vol. 187(C).
    8. Su, Liangjun & Lu, Xun, 2013. "Nonparametric dynamic panel data models: Kernel estimation and specification testing," Journal of Econometrics, Elsevier, vol. 176(2), pages 112-133.
    9. Fernandes, Marcelo & Grammig, Joachim, 2005. "Nonparametric specification tests for conditional duration models," Journal of Econometrics, Elsevier, vol. 127(1), pages 35-68, July.
    10. Inés Barbeito & Ricardo Cao & Stefan Sperlich, 2023. "Bandwidth selection for statistical matching and prediction," TEST: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 32(1), pages 418-446, March.
    11. repec:ebl:ecbull:v:3:y:2005:i:11:p:1-10 is not listed on IDEAS
    12. Hoderlein, Stefan & Su, Liangjun & White, Halbert & Yang, Thomas Tao, 2016. "Testing for monotonicity in unobservables under unconfoundedness," Journal of Econometrics, Elsevier, vol. 193(1), pages 183-202.
    13. Liu, Bo & Mojirsheibani, Majid, 2015. "On a weighted bootstrap approximation of the Lp norms of kernel density estimators," Statistics & Probability Letters, Elsevier, vol. 105(C), pages 65-73.
    14. Stefania D'Amico, 2004. "Density Estimation and Combination under Model Ambiguity," Computing in Economics and Finance 2004 273, Society for Computational Economics.
    15. Sami MESTIRI, 2022. "Modeling the volatility of Bitcoin returns using Nonparametric GARCH models," Journal of Academic Finance, RED research unit, university of Gabes, Tunisia, vol. 13(1), pages 2-16, June.
    16. Gozalo, Pedro L. & Linton, Oliver B., 2001. "Testing additivity in generalized nonparametric regression models with estimated parameters," Journal of Econometrics, Elsevier, vol. 104(1), pages 1-48, August.
    17. Paula Saavedra-Nieves & Rosa M. Crujeiras, 2022. "Nonparametric estimation of directional highest density regions," Advances in Data Analysis and Classification, Springer;German Classification Society - Gesellschaft für Klassifikation (GfKl);Japanese Classification Society (JCS);Classification and Data Analysis Group of the Italian Statistical Society (CLADAG);International Federation of Classification Societies (IFCS), vol. 16(3), pages 761-796, September.
    18. repec:cte:werepe:we1211 is not listed on IDEAS
    19. Centorrino, Samuele & Parmeter, Christopher F., 2024. "Nonparametric estimation of stochastic frontier models with weak separability," Journal of Econometrics, Elsevier, vol. 238(2).
    20. White, Halbert & Hong, Yongmiao, 1999. "M-Testing Using Finite and Infinite Dimensional Parameter Estimators," University of California at San Diego, Economics Working Paper Series qt9qz123ng, Department of Economics, UC San Diego.
    21. Masayuki Hirukawa & Mari Sakudo, 2016. "Testing Symmetry of Unknown Densities via Smoothing with the Generalized Gamma Kernels," Econometrics, MDPI, vol. 4(2), pages 1-27, June.
    22. Guo, Zheng-Feng & Shintani, Mototsugu, 2011. "Nonparametric lag selection for nonlinear additive autoregressive models," Economics Letters, Elsevier, vol. 111(2), pages 131-134, May.

    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:zbw:sfb373:199799. 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: ZBW - Leibniz Information Centre for Economics (email available below). General contact details of provider: https://edirc.repec.org/data/sfhubde.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.