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Simple and efficient improvements of multivariate local linear regression

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  • Cheng, Ming-Yen
  • Peng, Liang

Abstract

This paper studies improvements of multivariate local linear regression. Two intuitively appealing variance reduction techniques are proposed. They both yield estimators that retain the same asymptotic conditional bias as the multivariate local linear estimator and have smaller asymptotic conditional variances. The estimators are further examined in aspects of bandwidth selection, asymptotic relative efficiency and implementation. Their asymptotic relative efficiencies with respect to the multivariate local linear estimator are very attractive and increase exponentially as the number of covariates increases. Data-driven bandwidth selection procedures for the new estimators are straightforward given those for local linear regression. Since the proposed estimators each has a simple form, implementation is easy and requires much less or about the same amount of effort. In addition, boundary corrections are automatic as in the usual multivariate local linear regression.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:jmvana:v:97:y:2006:i:7:p:1501-1524
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    2. 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.
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