Title Page
Contents
ABSTRACT 8
Chapter 1. Introduction 9
Chapter 2. Graphical Models: Review 12
1. Graphical Models 12
2. Gaussian Graphical Models 13
Chapter 3. Estimation of the conditional independence 16
1. Neighborhood selection 16
2. Model selection criterion for neighborhood selection 17
Chapter 4. Numerical Study 19
1. Simulation studies 19
Chapter 5. Conclusion 38
References 39
Abstract(in Korean) 42
〈Table 4-1〉 Average of the sensitivity with the LASSO under Model 1 situation 22
〈Table 4-2〉 Average of the sensitivity with the SCAD under Model 1 situation 23
〈Table 4-3〉 Average of the specificity with the LASSO under Model 1 situation 24
〈Table 4-4〉 Average of the specificity with the SCAD under Model 1 situation 25
〈Table 4-5〉 Average of the sensitivity with the LASSO under AR(2) situation 26
〈Table 4-6〉 Average of the sensitivity with the SCAD under AR(2) situation 27
〈Table 4-7〉 Average of the specificity with the LASSO under AR(2) situation 28
〈Table 4-8〉 Average of the specificity with the SCAD under AR(2) situation 29
〈Figure 4-1〉 Sensitivity of AIC, BIC, and GIC₃ when sample size=100,200,300,400 in the Model 1 30
〈Figure 4-2〉 Sensitivity of GIC₄, GIC₅, GIC₆, and GIC₇ when sample size=100,200,300,400 in the Model 1 31
〈Figure 4-3〉 Specificity of AIC, BIC, and GIC₃ when sample size=100,200,300,400 in the Model 1 32
〈Figure 4-4〉 Specificity of GIC₄, GIC₅, GIC₆, and GIC₇ when sample size=100,200,300,400 in the Model 1 33
〈Figure 4-5〉 Sensitivity of AIC, BIC, and GIC₃ when sample size=100,200,300,400 in the AR(2) model 34
〈Figure 4-6〉 Sensitivity of GIC₄, GIC₅, GIC₆, and GIC₇ when sample size=100,200,300,400 in the AR(2) model 35
〈Figure 4-7〉 Specificity of AIC, BIC, and GIC₃ when sample size=100,200,300,400 in the AR(2) model 36
〈Figure 4-8〉 Specificity of GIC₄, GIC₅, GIC₆, and GIC₇ when sample size=100,200,300,400 in the AR(2) model 37