On Variance-Stabilizing Multivariate Non Parametric Regression Estimation

Kiheiji Nishida and Yuichiro Kanazawa

Communications in Statistics - Theory and Methods, 2015, vol. 44, issue 10, 2151-2175

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.

Date: 2015
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DOI: 10.1080/03610926.2013.775298

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