10.4225/03/59378e30aafac Ye, Azhong Azhong Ye Hyndman, Rob J. Rob J. Hyndman Li, Zinai Zinai Li Local linear multivariate regression with variable bandwidth in the presence of heteroscedasticity Monash University 2017 monash:7375 Heteroscedasticity Kernel smoothing 1959.1/42028 Local linear regression Variable bandwidth 2006 Plug-in bandwidth 2017-06-07 05:25:03 Journal contribution https://bridges.monash.edu/articles/journal_contribution/Local_linear_multivariate_regression_with_variable_bandwidth_in_the_presence_of_heteroscedasticity/5085253 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.