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|
|Open Access Date:||18 April 2019|
|Collection:||Thèses et mémoires|
All documents in CorpusUL are protected by Copyright Act of Canada.