 Multivariate bandwidth selection for local linear regressionLijian Yang and Rolf Tschernig () Journal of the Royal Statistical Society Series B, 1999, vol. 61, issue 4, 793-815 Abstract: 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. Date: 1999 Downloads: (external link) Related works: Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text Persistent link: https://EconPapers.repec.org/RePEc:bla:jorssb:v:61:y:1999:i:4:p:793-815 Ordering information: This journal article can be ordered from Access Statistics for this article Journal of the Royal Statistical Society Series B is currently edited by P. Fryzlewicz and I. Van Keilegom More articles in Journal of the Royal Statistical Society Series B from Royal Statistical Society Contact information at EDIRC. |
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