  Many spatial processes exhibit nonstationary features. We estimate a variance
function from a single process observation where the errors are nonstationary
and correlated. We propose a difference-based approach for a one-dimensional
nonstationary process and develop a bandwidth selection method for smoothing,
taking into account the correlation in the errors. The estimation results are
compared to that of a local-likelihood approach proposed by Anderes and
Stein(2011). A simulation study shows that our method has a smaller integrated
MSE, easily fixes the boundary bias problem, and requires far less computing
time than the likelihood-based method.
