Subsampling estimates of the Lasso distribution.

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A.2 Simulation code for the adaptive Lasso in a high dimensional setting 79 p_value,false_rejection_multiple, test_multiple,FWER,file= "simulation_low.RData"); A.2 Simulation code for the adaptive Lasso in a high dimensional setting library(mnormt); library(lars); library(Matrix); rm(list=ls(all=TRUE)); set.seed(10); ################################# ###### Setting parameters ###### p
80 R Codes ####################################################### ###### Outer loop - Replications of the scenario ###### for(k in 1:K) { x
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✄✄ ✄ ✄ ✄ ✄✄ ✄ ✄
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iv Abstract
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vi CONTENTS Contents Notation viii
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viii Notation List of Tables 6.1 Mo
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Chapter 1 Introduction In this thes
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Chapter 2 Minimizers of convex proc
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2.1 Convergence in probability 5 fo
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2.2 Convergence in distribution 7 a
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2.2 Convergence in distribution 9 L
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2.2 Convergence in distribution 11
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2.2 Convergence in distribution 13
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2.3 A continous mapping theorem for
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Page 28 and 29:
Page 30 and 31:
Chapter 3 Application to the Lasso
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3.2 Limit in distribution 23 almost
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3.2 Limit in distribution 25 We als
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3.2 Limit in distribution 27 3.2.2
Page 38 and 39: 3.2 Limit in distribution 29 Figure
Page 40 and 41: Chapter 4 The adaptive Lasso in a h
Page 42 and 43: 33 B.3 (Adaptive irrepresentable co
Page 44 and 45: 35 exists a constant K d depending
Page 46 and 47: 4.1 Variable selection consistency
Page 48 and 49: 4.2 Partial asymptotic normality 39
Page 50 and 51: 4.3 Marginal regressors as initial
Page 52 and 53: Chapter 5 Subsampling In his semina
Page 54 and 55: 5.1 Pointwise consistency for distr
Page 56 and 57: 5.2 Uniform consistency for quantil
Page 64 and 65: Chapter 6 Numerical results Motivat
Page 66 and 67: 6.1 Low dimensinal setting 57 5. De
Page 68 and 69: 6.1 Low dimensinal setting 59 Figur
Page 70 and 71: 6.2 High dimensional setting 61 3.
Page 72 and 73: 6.2 High dimensional setting 63 (d)
Page 74 and 75: 6.2 High dimensional setting 65 Mod
Page 76 and 77: 6.2 High dimensional setting 67 Mod
Page 78 and 79: 6.2 High dimensional setting 69 Fig
Page 80 and 81: Chapter 7 Concluding remarks We rev
Page 82 and 83: Bibliography Andersen, P. and R. Gi
Page 84 and 85: Appendix A R Codes A.1 Simulation c
Page 86 and 87: A.1 Simulation code for the Lasso i
Page 90 and 91: A.2 Simulation code for the adaptiv
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Subsampling estimates of the Lasso distribution.

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