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.