Reference : Contributions to spatial data analysis and Stein's method
Dissertations and theses : Doctoral thesis
Physical, chemical, mathematical & earth Sciences : Mathematics
Contributions to spatial data analysis and Stein's method
Ernst, Marie mailto [Université de Liège - ULiège > Département de mathématique > Département de mathématique >]
Université de Liège, ​Liège, ​​Belgique
Docteur en Sciences
Haesbroeck, Gentiane mailto
Swan, Yvik mailto
Lambert, Philippe mailto
Berckmoes, Ben
Ley, Christophe
Reinert, Gesine
[en] Spatial data analysis ; Robust statistics ; Local outliers ; Spatial autocorrelation ; Stein's method ; Covariance expansion ; Stein equations ; Stein factors ; Total variation distance ; Wasserstein distance ; Kolmogorov distance ; Integral probability metrics
[en] The thesis consists of two parts.
The first part is rooted in robust statistics, and more precisely in local outlier detection in spatial multivariate data, and the robustness of tests concerning autocorrelation.
The second part deals with the probabilistic method developed by Charles Stein. In the thesis, Stein's method was linked to first order covariance relations, infinite covariance expansions, and distances between probability distributions.

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