000100027 001__ 100027
000100027 005__ 20190509132120.0
000100027 0247_ $$2doi$$a10.5075/epfl-thesis-3758
000100027 02470 $$2urn$$aurn:nbn:ch:bel-epfl-thesis3758-1
000100027 02471 $$2nebis$$a5296287
000100027 037__ $$aTHESIS
000100027 041__ $$afre
000100027 088__ $$a3758
000100027 245__ $$aPrédiction spatiale en présence d'erreurs substitutives et modélisation par drap stable
000100027 269__ $$a2007
000100027 260__ $$bEPFL$$c2007$$aLausanne
000100027 300__ $$a140
000100027 336__ $$aTheses
000100027 502__ $$aAndreas Papritz, Anthony C. Davison, Marc Genton
000100027 520__ $$aIn geostatistics, the presence of outlying data is more the rule than the exception. Moreover, the statistical analysis of data contaminated by outliers requires caution, particularly when a spatial dependence exists. In order to take into account these possible outliers during the adjustment of the spatial process, a new modeling tool, called the substitutive errors model, is proposed. The optimal prediction in the least squares sense is derived and its properties are studied. Because of its complexity, this estimator needs in practice to be numerically approximated. An automated algorithm is proposed in this thesis. This method is based on an ordering of the observations with respect to the specified spatial process of interest, with the values least in agreement being included towards the end of the ordering. It proves to be useful in case of masked multiple outliers or nonstationary clusters. Simulations are carried out to illustrate its performances and to compare it to other forecasts, robust or not. An application to real data is provided as an illustration of its practical usefulness. The second part of this work also deals with the presence of spatial heterogeneity. One could say that the proposed model offers a characterization of this heterogeneity rather than estimating the locations and sizes of outliers. It is based on the theory of bidimensional α-stable motion. This represents a generalization of the unidimensional Brownian motion. In particular, the stability parameter α can be seen as a measure of the distance between the observations and the hypothesis of a Gaussian distribution. A method of estimation for the parameters of such a process is presented, based on a numerical constrained optimization of the likelihood. Its performances are illustrated by means of simulations. An application ends this second part.
000100027 6531_ $$abidimensional a-stable motion
000100027 6531_ $$aforward search
000100027 6531_ $$ageostatistics
000100027 6531_ $$aheterogeneity
000100027 6531_ $$arobust kriging
000100027 6531_ $$asubstitutive errors
000100027 6531_ $$aerreurs substitutives
000100027 6531_ $$agéostatistique
000100027 6531_ $$ahétérogénéité
000100027 6531_ $$améthode forward search
000100027 6531_ $$amouvement a-stable bidimensionnel
000100027 6531_ $$akrigeage robuste
000100027 700__ $$0(EPFLAUTH)111248$$g111248$$aFournier, Baptiste
000100027 720_2 $$aMorgenthaler, Stephan$$edir.$$g105911$$0241889
000100027 8564_ $$uhttps://infoscience.epfl.ch/record/100027/files/EPFL_TH3758.pdf$$zTexte intégral / Full text$$s27555726$$yTexte intégral / Full text
000100027 909C0 $$xU10127$$0252209$$pSTAP
000100027 909CO $$pthesis-bn2018$$pDOI$$pSB$$ooai:infoscience.tind.io:100027$$qDOI2$$qGLOBAL_SET$$pthesis
000100027 918__ $$bSB-SMA$$cIMA$$aSB
000100027 919__ $$aSTAP
000100027 920__ $$b2007$$a2007-4-20
000100027 970__ $$a3758/THESES
000100027 973__ $$sPUBLISHED$$aEPFL
000100027 980__ $$aTHESIS