PMID- 25580039
OWN - NLM
STAT- PubMed-not-MEDLINE
LR  - 20240322
IS  - 0090-5364 (Print)
IS  - 0090-5364 (Linking)
VI  - 42
IP  - 1
DP  - 2014 Feb 1
TI  - ADAPTIVE ROBUST VARIABLE SELECTION.
PG  - 324-351
AB  - Heavy-tailed high-dimensional data are commonly encountered in various scientific 
      fields and pose great challenges to modern statistical analysis. A natural 
      procedure to address this problem is to use penalized quantile regression with 
      weighted L(1)-penalty, called weighted robust Lasso (WR-Lasso), in which weights 
      are introduced to ameliorate the bias problem induced by the L(1)-penalty. In the 
      ultra-high dimensional setting, where the dimensionality can grow exponentially 
      with the sample size, we investigate the model selection oracle property and 
      establish the asymptotic normality of the WR-Lasso. We show that only mild 
      conditions on the model error distribution are needed. Our theoretical results 
      also reveal that adaptive choice of the weight vector is essential for the 
      WR-Lasso to enjoy these nice asymptotic properties. To make the WR-Lasso 
      practically feasible, we propose a two-step procedure, called adaptive robust 
      Lasso (AR-Lasso), in which the weight vector in the second step is constructed 
      based on the L(1)-penalized quantile regression estimate from the first step. 
      This two-step procedure is justified theoretically to possess the oracle property 
      and the asymptotic normality. Numerical studies demonstrate the favorable 
      finite-sample performance of the AR-Lasso.
FAU - Fan, Jianqing
AU  - Fan J
AD  - Princeton University, University of Southern California and IBM T.J. Watson 
      Research Center.
FAU - Fan, Yingying
AU  - Fan Y
AD  - Princeton University, University of Southern California and IBM T.J. Watson 
      Research Center.
FAU - Barut, Emre
AU  - Barut E
AD  - Princeton University, University of Southern California and IBM T.J. Watson 
      Research Center.
LA  - eng
GR  - R01 GM072611/GM/NIGMS NIH HHS/United States
PT  - Journal Article
PL  - United States
TA  - Ann Stat
JT  - Annals of statistics
JID - 0365252
PMC - PMC4286898
MID - NIHMS649191
OTO - NOTNLM
OT  - Adaptive weighted L1
OT  - High dimensions
OT  - Oracle properties
OT  - Robust regularization
EDAT- 2015/01/13 06:00
MHDA- 2015/01/13 06:01
PMCR- 2015/01/08
CRDT- 2015/01/13 06:00
PHST- 2015/01/13 06:00 [entrez]
PHST- 2015/01/13 06:00 [pubmed]
PHST- 2015/01/13 06:01 [medline]
PHST- 2015/01/08 00:00 [pmc-release]
AID - 10.1214/13-AOS1191 [doi]
PST - ppublish
SO  - Ann Stat. 2014 Feb 1;42(1):324-351. doi: 10.1214/13-AOS1191.