One-dimensional Nonstationary Process Variance Function Estimation
  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. 
Eunice J. Kim and Zhengyuan Zhu
stat.ME