The lq consistency of the Dantzig selector for Cox's proportional hazards model

Kou Fujimori; Yoichi Nishiyama

doi:10.1016/j.jspi.2016.09.004

The l_q consistency of the Dantzig selector for Cox's proportional hazards model

Kou Fujimori^*, Yoichi Nishiyama

^*Corresponding author for this work

School of International Liberal Studies

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

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 l_q 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.

Original language	English
Pages (from-to)	62-70
Number of pages	9
Journal	Journal of Statistical Planning and Inference
Volume	181
DOIs	https://doi.org/10.1016/j.jspi.2016.09.004
Publication status	Published - 2017 Feb 1

Keywords

Consistency
Dantzig selector
Proportional hazards model

ASJC Scopus subject areas

Statistics and Probability
Statistics, Probability and Uncertainty
Applied Mathematics

Access to Document

10.1016/j.jspi.2016.09.004

Cite this

@article{fab6d1de04d044268b7aa19d5a59d875,

title = "The lq consistency of the Dantzig selector for Cox's proportional hazards model",

abstract = "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.",

keywords = "Consistency, Dantzig selector, Proportional hazards model",

author = "Kou Fujimori and Yoichi Nishiyama",

note = "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{\textquoteright}s work was supported by Grant-in-Aid for Scientific Research (C), 15K00062 , from Japan Society for the Promotion of Science . Publisher Copyright: {\textcopyright} 2016 Elsevier B.V.",

year = "2017",

month = feb,

day = "1",

doi = "10.1016/j.jspi.2016.09.004",

language = "English",

volume = "181",

pages = "62--70",

journal = "Journal of Statistical Planning and Inference",

issn = "0378-3758",

publisher = "Elsevier",

}

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

UR - http://www.scopus.com/inward/record.url?scp=84994667211&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84994667211&partnerID=8YFLogxK

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 -