Title Page
Abstract
Contents
Chapter 1. INTRODUCTION 9
Chapter 2. Lasso Regression 11
2.1. The Lasso estimator 11
2.2. Adaptive Lasso 12
2.3. Elastic net 13
2.4. Lasso for Generalized Linear Models 13
2.4.1. Logistic regression 15
Chapter 3. FDR control via data splitting 16
3.1. Multiple testing 16
3.2. BHq procedure 18
3.3. FDR control in Regression models 19
3.4. Single Data Splitting(DS) 19
3.5. Multiple Data Splitting(MDS) 21
3.6. Application for linear models 22
Chapter 4. Simulation Study 23
4.1. Lasso vs Adaptive Lasso 23
4.2. DS vs MDS 24
Chapter 5. R Code 28
Chapter 6. Conclusion 31
Bibliography 32
초록 34
Table 3.1. The possible outcomes when testing multiple null hypotheses. 17
Figure 4.1. Estimated regression coefficients using lasso and adaptive lasso 24
Figure 4.2. ρ=0,0.3 with δ=3, n=500, p=500, p₁=50 25
Figure 4.3. ρ=0.5, 0.8 with δ=3, n=500, p=500, p₁=50 25
Figure 4.4. ρ=0, 0.3 with δ=3, n=500, p=1000, p₁=100 26
Figure 4.5. ρ=0.5, 0.8 with δ=3, n=500, p=1000, p₁=100 26