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Multivariate plug-in bandwidth for local linear regression

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  • 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
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    References listed on IDEAS

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    1. 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.
    2. 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.
    3. 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.
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