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4 Motivation: ”Omics” Data in Population-Based Studies • In genome-wide assocation studies, a million SNP markers are genotyped across the genome to study the association of common genetic variants and disease phenotypes (case/control status). • The massive whole genome-wide sequencing data are rapidly available, e.g., the 1000 genome project, to study the effects of rare variants. March, 2009 Xihong Lin
5 Motivation • Variable selection is of significant interests in current biomedical ”omics” studies. • Common variable selection approaches are penalized likelihood based, e.g., LASSO, adaptive LASSO and SCAD. • The Dantzig selector (DS; Candes and Tao, 2007) can be viewed as an estimating equation based variable selection procedure and is particularly appealing for longitudinal data. • Little is known about the asymptotic properties of the DS. • Focus of this talk (Independent data): (1) Large sample properties of the DS. (2) Propose Adaptive DS. (3) Connection with Adaptive Lasso. March, 2009 Xihong Lin
Page 1 and 2: 1 Variable Selection Using the Dant
Page 3: 3 Motivation: ”Omics” Data in P
Page 7 and 8: 7 Model Setup Model: y i = X T i β
Page 9 and 10: 9 Dantzig Selector • Idea: Rather
Page 11 and 12: 11 Uniqueness and the Dantzig Selec
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

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