Surface estimation under local stationarity

Abstract

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.

Keywords:

• hermite polynomials
• kernel smoothing
• long memory
• short memory
• local stationarity

Acknowledgments

The ozone data set used in this paper was downloaded by Dr Dieter Schell (University of Konstanz) from the homepage of NASA, ozone processing unit. The author is also grateful for the careful reading and very helpful remarks by two referees, which led to a significant improvement of the manuscript.

Disclosure statement

No potential conflict of interest was reported by the author.