Wavelet nonparametric estimation from strong spatial correlated high-dimensional data

This paper addresses the problem of spatial prediction from strong spatial correlated high-dimensional data. Two approaches are considered: spatial wavelet kernel penalized nonparametric regression, and wavelet shrinkage. The best performance corresponds to spatial wavelet thresholding techniques applied to coarser scales, when slowly varying data displaying strong spatial correlations are analyzed. Our initial motivation relies on spatial estimation of annual mean ocean surface temperature maps to detect changes in ocean-surface temperatures, that could cause modifications in atmospheric circulation and precipitation. Specifically, we have analyzed daily ocean surface temperature curves from the Hawaii ocean stations, available at latitude-longitude interval [22.7,22.8]×[−158.1,−157.94] during the period 2000-2007, from The World-Wide Ocean Optics Database (WOOD). Additionally, wavelet-based non-linear estimation procedures are compared with wavelet-based Gaussian linear model estimation methods, based on spatial autoregressive Hilbertian processes, and heavy tail covariance processes, solution to fractional pseudodifferential equations.