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bootstrap, penalized log-likelihood, graphical model, glasso, estimate evaluation

Zhu, Yunan

Supervisor and department: Karunamuni, Rohana Mathematical and Statistical Sciences Cribben, Ivor Finance and Statistical Analysis

Examining committee member and department: Karunamuni, Rohana Mathematical and Statistical Sciences Yuan, Yan Public Health Frei, Christoph Mathematical and Statistical Sciences Jiang, Bei Mathematical and Statistical Sciences Cribben, Ivor Finance and Statistical Analysis

Department: Department of Mathematical and Statistical Sciences

Specialization: Statistics

Date accepted: 2015-09-30T09:22:04Z

Graduation date: 2015-11

Degree: Master of Science

Degree level: Master's

Abstract: Graphical models are frequently used to explore networks among a set of variables. Several methods for estimating sparse graphs have been proposed and their theoretical properties have been explored. There are also several selection criteria to select the optimal estimated models. However, their practical performance has not been studied in detail. In this work, several estimation procedures glasso, bootstrap glasso, adptive lasso, SCAD, DP-glasso and Huge and several selection criteria AIC, BIC, CV, ebic, ric and stars are compared under various simulation settings, such as different dimensions or sample sizes, different types of data, and different sparsity levels of the true model structures. Then we use several evaluation criteria to compare the optimal estimated models and discuss in detail the superiority and deficiency of each combination of estimating methods and selection criteria.

Language: English

DOI: doi:10.7939-R3F766G1T

Rights: Permission is hereby granted to the University of Alberta Libraries to reproduce single copies of this thesis and to lend or sell such copies for private, scholarly or scientific research purposes only. The author reserves all other publication and other rights in association with the copyright in the thesis and, except as herein before provided, neither the thesis nor any substantial portion thereof may be printed or otherwise reproduced in any material form whatsoever without the author's prior written permission.





Autor: Zhu, Yunan

Fuente: https://era.library.ualberta.ca/


Introducción



Estimating Sparse Graphical Models: Insights Through Simulation by Yunan Zhu A thesis submitted in partial fulfillment of the requirements for the degree of Master of Science in STATISTICS Department of Mathematical and Statistical Sciences Faculty of Science University of Alberta © Yunan Zhu, 2015 ii Abstract Graphical models are frequently used to explore networks among a set of variables.
Several methods for estimating sparse graphs have been proposed and their theoretical properties have been explored.
There are also several selection criteria to select the optimal estimated models.
However, their practical performance has not been studied in detail.
In this work, several estimation procedures (glasso, bootstrap glasso, adptive lasso, SCAD, DP-glasso and Huge) and several selection criteria (AIC, BIC, CV, ebic, ric and stars) are compared under various simulation settings, such as different dimensions or sample sizes, different types of data, and different sparsity levels of the true model structures.
Then we use several evaluation criteria to compare the optimal estimated models and discuss in detail the superiority and deficiency of each combination of estimating methods and selection criteria. iii Acknowledgment First and foremost, I express herein my deepest gratitude to my co-supervisors Dr.
Ivor Cribben and Prof.
Dr.
Rohana Karunamuni for their guidence and support throughout my graduate studies. After being brought to U of A by Dr.
Karunamuni, my life as a graduate student started with a knowledgable and patient mentor.
All sorts of difficulties, confusion and challenges happened to me during the last two years but, however, Dr.
Karunamuni was the one who always sent me quiet but strong support to lift me up to a new stage.
I thank Dr.
Karunamuni for any of his continual attention to, interest in and concerns with my coursework and research, thought I have not had a chance to take a course with this excellent professor. At the same time, D...





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