On Variance-Stabilizing Multivariate Non Parametric Regression Estimation |
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Authors: | Kiheiji Nishida Yuichiro Kanazawa |
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Institution: | 1. Graduate School of Medicine, Osaka University, Suita, Osaka, Japankiheiji.nishida@gmail.com;3. Graduate School of Systems and Information Engineering, University of Tsukuba, Tsukuba, Ibaraki, Japan |
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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. |
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Keywords: | Bandwidth selection Local linear estimator Local variable bandwidth Variance-stabilization |
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