Faculté des Sciences
##### MASTER THESIS
VIEW 95 | DOWNLOAD 30

### Stein factors for absolutely continuous distributions with interval support and applications.

##### Details
 Title : Stein factors for absolutely continuous distributions with interval support and applications. Translated title : [fr] Facteurs de Stein pour les distributions absolument continues à support compact et applications Author : Plomteux, Adrien Date of defense  : 28-Jun-2017 Advisor(s) : Swan, Yvik Committee's member(s) : Haesbroeck, Gentiane  Mijoule, Guillaume  Nicolay, Samuel  Schneiders, Jean-Pierre Language : English Number of pages : 139 Keywords : [en] Stein factors[en] Stein's method[en] Central Limit Theorem Discipline(s) : Physical, chemical, mathematical & earth Sciences > Mathematics Institution(s) : Université de Liège, Liège, Belgique Degree: Master en sciences mathématiques, à finalité spécialisée en statistique Faculty: Master thesis of the Faculté des Sciences

##### Abstract

[en] The purpose of this work is to provide Stein factors for absolutely continuous distributions with interval support. It is divided into two parts. The first part provide the general theory that will eventually yield Stein factors whereas the second part consist in applications.

In the theory part, we basically follow the Stein’s method, i.e. give a Stein characterisation, the Stein equation and the Stein solution to finally give Stein factors. We first follow this procedure for the special case of the normal distribution and then for the more general case of absolutely continuous distributions with interval support.

In the application part, we first apply the general theory in the normal, beta, gamma and Student cases. In order to apply the factors obtained, we provide some theories enabling to use them to bound the Wasserstein distance; hence we give a theory for the general case as well as zero-bias, K-function and exchangeable pairs methods for the more specific normal case. In particular and among others, we find an upper bound of the rate of convergence of the Student distribution towards the Gaussian and also find upper bounds on the rates of convergence of the Central Limit Theorem in the exponential and Bernoulli cases. For each of these applications, we find bounds with the same order as the Berry-Esseen theorem.

### Document(s)

Memoire_Plomteux.pdf
Description:
Size: 2.46 MB
Format: Adobe PDF

### Author

• Plomteux, Adrien Université de Liège > Master sc. math., à fin.

### Committee's member(s)

• Haesbroeck, Gentiane Université de Liège - ULg > Département de mathématique > Statistique mathématique
View his publications on ORBi
• Mijoule, Guillaume Université de Liège - ULg > Département de mathématique > Probabilités et statistique mathématique
View his publications on ORBi
• Nicolay, Samuel Université de Liège - ULg > Département de mathématique > Analyse - Analyse fonctionnelle - Ondelettes
View his publications on ORBi
• Schneiders, Jean-Pierre Université de Liège - ULg > Département de mathématique > Analyse algébrique
View his publications on ORBi
• Total number of views 95
• Total number of downloads 30

All documents available on MatheO are protected by copyright and subject to the usual rules for fair use.
The University of Liège does not guarantee the scientific quality of these students' works or the accuracy of all the information they contain.