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On Variance-Stabilizing Multivariate Non Parametric Regression Estimation

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  • Kiheiji Nishida
  • Yuichiro Kanazawa

Abstract

The mean squared error (MSE)-minimizing local variable bandwidth for the univariate local linear estimator (the LL) is well-known. This bandwidth does not stabilize variance over the domain. Moreover, in regions where a regression function has zero curvature, the LL estimator is discontinuous. In this paper, we propose a variance-stabilizing (VS) local variable diagonal bandwidth matrix for the multivariate LL estimator. Theoretically, the VS bandwidth can outperform the multivariate extension of the MSE-minimizing local variable scalar bandwidth in terms of asymptotic mean integrated squared error and can avoid discontinuity created by the MSE-minimizing bandwidth. We present an algorithm for estimating the VS bandwidth and simulation studies.

Suggested Citation

  • Kiheiji Nishida & Yuichiro Kanazawa, 2015. "On Variance-Stabilizing Multivariate Non Parametric Regression Estimation," Communications in Statistics - Theory and Methods, Taylor & Francis Journals, vol. 44(10), pages 2151-2175, May.
    • Handle: RePEc:taf:lstaxx:v:44:y:2015:i:10:p:2151-2175
    DOI: 10.1080/03610926.2013.775298
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