On Variance Estimation for Nonparametric Surface Estimates Under Gaussian Subordination

• Activity Number: 497
• Type: Contributed
• Date/Time: Wednesday, August 6, 2014 : 10:30 AM to 12:20 PM
• Sponsor: IMS
• Author(s): Sucharita Ghosh*+
• Companies: Swiss Federal Research Institute WSL
• Keywords: Hermite polynomials ; Kernel smoothing ; Spatial data ; Short memory ; Long memory ; Local stationarity

Abstract

We consider nonparametric surface estimation in a regression model with non-Gaussian errors that are an unknown transformation of a latent zero mean, stationary Gaussian random field. For the time series case, Ghosh and Draghicescu (2002) give a sketch of a bandwidth selection algorithm via a direct variance estimation method for trend estimates. In this talk, considering kernels that satisfy the conditions of Parzen (1962), we give a simple proof of uniform convergence in probability of the nonparametric surface estimator. We consider both short memory and long memory correlations in the latent spatial Gaussian random field. We then note that under suitable regularity conditions, a potential variance estimation procedure along the lines of Ghosh and Draghicescu (2002) emerges, which relies on the local stationarity type property of the error process. An excerpt from a global total column ozone data set on a regular grid (source: NASA) is used to motivate discussions.