Azhong Ye1 , Rob J Hyndman2 and Zinai Li3
- College of Management, Fuzhou University, Fuzhou, 350002, China.
- Department of Econometrics and Business Statistics, Monash University, VIC 3800, Australia.
- School of Economics and Management, Tsinghua University, Beijing, 100084, China.
Abstract We present a local linear estimator with variable bandwidth for multivariate nonparametric 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.
Keywords: heteroscedasticity; kernel smoothing; local linear regression; plug-in bandwidth, variable bandwidth.