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Multivariate bandwidth selection for local linear regression


  • L. Yang
  • R. Tschernig


The existence and properties of optimal bandwidths for multivariate local linear regression are established, using either a scalar bandwidth for all regressors or a diagonal bandwidth vector that has a different bandwidth for each regressor. Both involve functionals of the derivatives of the unknown multivariate regression function. Estimating these functionals is difficult primarily because they contain multivariate derivatives. In this paper, an estimator of the multivariate second derivative is obtained via local cubic regression with most cross‐terms left out. This estimator has the optimal rate of convergence but is simpler and uses much less computing time than the full local estimator. Using this as a pilot estimator, we obtain plug‐in formulae for the optimal bandwidth, both scalar and diagonal, for multivariate local linear regression. As a simpler alternative, we also provide rule‐of‐thumb bandwidth selectors. All these bandwidths have satisfactory performance in our simulation study.

Suggested Citation

  • L. Yang & R. Tschernig, 1999. "Multivariate bandwidth selection for local linear regression," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 61(4), pages 793-815.
  • Handle: RePEc:bla:jorssb:v:61:y:1999:i:4:p:793-815

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    10. Giordano, Francesco & Parrella, Maria Lucia, 2016. "Bias-corrected inference for multivariate nonparametric regression: Model selection and oracle property," Journal of Multivariate Analysis, Elsevier, vol. 143(C), pages 71-93.
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    12. CHIKHI, Mohamed, 2009. "Identification non paramétrique d’un processus non linéaire hétéroscédastique
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    16. Andrews, Donald W.K. & Shi, Xiaoxia, 2014. "Nonparametric inference based on conditional moment inequalities," Journal of Econometrics, Elsevier, vol. 179(1), pages 31-45.
    17. Chevallier, Julien, 2011. "Nonparametric modeling of carbon prices," Energy Economics, Elsevier, vol. 33(6), pages 1267-1282.
    18. Francesco Giordano & Maria Lucia Parrella, 2014. "Bias-corrected inference for multivariate nonparametric regression: model selection and oracle property," Working Papers 3_232, Dipartimento di Scienze Economiche e Statistiche, Università degli Studi di Salerno.
    19. Rolf Tschernig & Lijian Yang, 2000. "Nonparametric Estimation of Generalized Impulse Response Functions," Econometric Society World Congress 2000 Contributed Papers 1417, Econometric Society.
    20. Naito, Kanta & Yoshizaki, Masahiro, 2009. "Bandwidth selection for a data sharpening estimator in nonparametric regression," Journal of Multivariate Analysis, Elsevier, vol. 100(7), pages 1465-1486, August.
    21. Wolfgang Härdle & Torsten Kleinow & Rolf Tschernig, 2001. "Web Quantlets for Time Series Analysis," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 179-188, March.
    22. Hupfeld, Stefan, 2009. "Rich and healthy--better than poor and sick?: An empirical analysis of income, health, and the duration of the pension benefit spell," Journal of Health Economics, Elsevier, vol. 28(2), pages 427-443, March.
    23. CHIKHI, Mohamed, 2017. "Chocs exogènes et non linéarités dans les séries boursières: Application à la modélisation non paramétrique du cours de l'action Orange
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    24. Qi Li & Jeffrey Scott Racine, 2006. "Nonparametric Econometrics: Theory and Practice," Economics Books, Princeton University Press, edition 1, number 8355, November.
    25. Cheng, Ming-Yen & Peng, Liang, 2006. "Simple and efficient improvements of multivariate local linear regression," Journal of Multivariate Analysis, Elsevier, vol. 97(7), pages 1501-1524, August.

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