Slides

More documents

Recommendations

Info

10 Questions • Question(s) 1: Is the Dantzig selector consistent for estimation? What is its asymptotic distribution? • Question 2: Is the Dantzig selector consistent for model selection? i.e., is lim P( ˆT = T ∗ ) = 1? n→∞ • Answers to Questions 1 and 2 depend heavily on choice of λ. • When does the Dantzig selector have a unique solution? March, 2009 Xihong Lin
11 Uniqueness and the Dantzig Selector D β^ || β^ || 1 B 1 • The DS feasible set: D = {β; ||X ′ (y − Xβ)|| ∞ ≤ λ} • If D is not parallel to the closed L 1 -unit ball, B 1 , then the Dantzig selector has a unique solution. • If X i are iid then the Dantzig selector has a unique solution with probability 1. March, 2009 Xihong Lin
Page 1 and 2: 1 Variable Selection Using the Dant
Page 3 and 4: 3 Motivation: ”Omics” Data in P
Page 5 and 6: 5 Motivation • Variable selection
Page 7 and 8: 7 Model Setup Model: y i = X T i β
Page 9: 9 Dantzig Selector • Idea: Rather
Page 13 and 14: 13 Asymptotic Properties of the Dan
Page 15 and 16: 15 Adaptive Dantzig Selector Dantzi
Page 17 and 18: 17 Adaptive Dantzig Selector and Ad
Page 19 and 20: 19 Estimation of the Toning Paramet
Page 21 and 22: 21 Simulation Settings • Simulati
Page 23: 23 Concluding Remarks • Adaptive

Slides

Create successful ePaper yourself

Delete template?

Save as template?