Variance function estimation of a one-dimensional nonstationary process
We propose a flexible nonparametric estimation of a variance function from a one-dimensional process where the process errors are nonstationary and correlated. Due to nonstationarity a local variogram is defined, and its asymptotic properties are derived. We include a bandwidth selection method for smoothing taking into account the correlations in the errors. We compare the proposed difference-based nonparametric approach with Anderes and Stein(2011)’s local-likelihood approach. Our method has a smaller integrated MSE, easily fixes the boundary bias, and requires far less computing time than the likelihood-based method.
This is a manuscript of an article published as Kim, Eunice J., and Zhengyuan Zhu. "Variance function estimation of a one-dimensional nonstationary process." Journal of the Korean Statistical Society (2019). doi: 10.1016/j.jkss.2019.01.001. Posted with permission.