Local linear multivariate regression with variable bandwidth in the presence of heteroscedasticity
journal contributionposted on 07.06.2017 by Ye, Azhong, Hyndman, Rob J., Li, Zinai
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We present a local linear estimator with variable bandwidth for multivariate non-parametric regression. We prove its consistency and asymptotic normality in the interior of the observed data and obtain its rates of convergence. This result is used to obtain practical direct plug-in bandwidth selectors for heteroscedastic regression in one and two dimensions. We show that the local linear estimator with variable bandwidth has better goodness-of-fit properties than the local linear estimator with constant bandwidth, in the presence of heteroscedasticity.