La fonction de profondeur de Tukey

Authors: Cisse, Mouhamadou Moustapha
Advisor: Ransford, Thomas Joseph
Abstract: In this memoir we define the Tukey depth function of a positive finite measure on Rd. Then we study the properties of this function, in particular the properties of continuity and convexity. We seek to establish a characterization of a measure by its depth function. That is, given μ, v finite positive measures on Rd, do we have μ = v if μ and v have the same Tukey depth function? We use the properties of the depth function to establish such a characterization when the measure satisfies certain geometric properties. Then we exhibit some approaches for computing the Tukey depth function. Finally we prove the theorem of characterisation of a discrete measure by its Tukey depth function.
Document Type: Mémoire de maîtrise
Issue Date: 2019
Open Access Date: 18 April 2019
Grantor: Université Laval
Collection:Thèses et mémoires

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