TY - JOUR
T1 - The lq consistency of the Dantzig selector for Cox's proportional hazards model
AU - Fujimori, Kou
AU - Nishiyama, Yoichi
N1 - Funding Information:
We are grateful to the Associate Editor and the referees for useful comments. Especially, we have been able to prove the l ∞ consistency of DSfPH inspired by their comments. The second author’s work was supported by Grant-in-Aid for Scientific Research (C), 15K00062 , from Japan Society for the Promotion of Science .
Publisher Copyright:
© 2016 Elsevier B.V.
PY - 2017/2/1
Y1 - 2017/2/1
N2 - The Dantzig selector for the proportional hazards model proposed by D.R. Cox is studied in a high-dimensional and sparse setting. We prove the lq consistency for all q∈[1,∞] of some estimators based on the compatibility factor, the weak cone invertibility factor, and the restricted eigenvalue for certain deterministic matrix which approximates the Hessian matrix of log partial likelihood. Our matrix conditions for these factors are weaker than those of previous researches.
AB - The Dantzig selector for the proportional hazards model proposed by D.R. Cox is studied in a high-dimensional and sparse setting. We prove the lq consistency for all q∈[1,∞] of some estimators based on the compatibility factor, the weak cone invertibility factor, and the restricted eigenvalue for certain deterministic matrix which approximates the Hessian matrix of log partial likelihood. Our matrix conditions for these factors are weaker than those of previous researches.
KW - Consistency
KW - Dantzig selector
KW - Proportional hazards model
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U2 - 10.1016/j.jspi.2016.09.004
DO - 10.1016/j.jspi.2016.09.004
M3 - Article
AN - SCOPUS:84994667211
SN - 0378-3758
VL - 181
SP - 62
EP - 70
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
ER -