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Title of Journal: Stoch Environ Res Risk Assess

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Abbravation: Stochastic Environmental Research and Risk Assessment

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Springer Berlin Heidelberg

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DOI

10.1002/acs.682

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1436-3259

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Moment and Bayesian wavelet regression from spatia

Authors: R M FernándezPascual R Espejo M D RuizMedina
Publish Date: 2015/08/08
Volume: 30, Issue: 2, Pages: 523-557
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Abstract

A new waveletbased estimation methodology in the context of spatial functional regression is proposed to discriminate between smallscale and large scale variability of spatially correlated functional data defined by depthdependent curves Specifically the discrete wavelet transform of the data is computed in space and depth to reduce dimensionality Momentbased regression estimation is applied for the approximation of the scaling coefficients of the functional response While its wavelet coefficients are estimated in a Bayesian regression framework Both regression approaches are implemented from the empirical versions of the scaling and wavelet autocovariance and crosscovariance operators characterizing the correlation structure of the spatial functional response Weather stations in ocean islands display high spatial concentration The proposed estimation methodology overcomes the difficulties arising in the estimation of ocean temperature field at different depths from long records of ocean temperature measurements in these stations Data are collected from The WorldWide Ocean Optics Database The performance of the presented approach is tested in terms of 10fold crossvalidation and residual spatial and depth correlation analysis Additionally an application to soil sciences for prediction of electrical conductivity profiles is also considered to compare this approach with previous related ones in the statistical analysis of spatially correlated curves in depthThis work has been supported in part by project MTM201232674 cofunded with FEDER of the DGI MEC Spain We would like to thank Professors Yang Wikley Holanz Myersx and Sudduth for sending and allowing us to use their dataset to illustrate the estimation methodology proposed in this paper which has been inspired and motivated by their proposal


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