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Challenging the curse of dimensionality in multivariate local linear regression.

Taylor, James and Einbeck, Jochen (2013) 'Challenging the curse of dimensionality in multivariate local linear regression.', Computational statistics., 28 (3). pp. 955-976.


Local polynomial fitting for univariate data has been widely studied and discussed, but up until now the multivariate equivalent has often been deemed impractical, due to the so-called curse of dimensionality. Here, rather than discounting it completely, we use density as a threshold to determine where over a data range reliable multivariate smoothing is possible, whilst accepting that in large areas it is not. The merits of a density threshold derived from the asymptotic influence function are shown using both real and simulated data sets. Further, the challenging issue of multivariate bandwidth selection, which is known to be affected detrimentally by sparse data which inevitably arise in higher dimensions, is considered. In an effort to alleviate this problem, two adaptations to generalized cross-validation are implemented, and a simulation study is presented to support the proposed method. It is also discussed how the density threshold and the adapted generalized cross-validation technique introduced herein work neatly together.

Item Type:Article
Keywords:Multivariate smoothing, Density estimation, Bandwidth selection, Influence function.
Full text:(AM) Accepted Manuscript
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Publisher statement:The final publication is available at Springer via
Date accepted:No date available
Date deposited:23 September 2014
Date of first online publication:June 2013
Date first made open access:No date available

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