Surface estimation under local stationarity

摘要

Consider a nonparametric regression model involving spatial observations that are nonlinear transformations of a latent Gaussian random field. We address estimation of the variance of the Priestley-Chao kernel estimator of the surface by using a local stationarity-type property which is a result of the assumed transformation. It turns out that it is possible to avoid estimation of the various nuisance parameters so as to estimate the leading term of the asymptotic variance of the estimator. We also address uniform convergence of the nonparametric surface estimator, under short-memory and long-memory correlations in the data.