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Article: A new MM algorithm for constrained estimation in the proportional hazards model

TitleA new MM algorithm for constrained estimation in the proportional hazards model
Authors
KeywordsAsymptotic properties
Bootstrap approach
Constrained estimation
Karush-Kuhn-Tucker conditions
MM algorithm
Proportional hazards model
Issue Date2015
PublisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/csda
Citation
Computational Statistics & Data Analysis, 2015, v. 84, p. 135-151 How to Cite?
AbstractThe constrained estimation in Cox’s model for the right-censored survival data is studied and the asymptotic properties of the constrained estimators are derived by using the Lagrangian method based on Karush–Kuhn–Tucker conditions. A novel minorization–maximization (MM) algorithm is developed for calculating the maximum likelihood estimates of the regression coefficients subject to box or linear inequality restrictions in the proportional hazards model. The first M-step of the proposed MM algorithm is to construct a surrogate function with a diagonal Hessian matrix, which can be reached by utilizing the convexity of the exponential function and the negative logarithm function. The second M-step is to maximize the surrogate function with a diagonal Hessian matrix subject to box constraints, which is equivalent to separately maximizing several one-dimensional concave functions with a lower bound and an upper bound constraint, resulting in an explicit solution via a median function. The ascent property of the proposed MM algorithm under constraints is theoretically justified. Standard error estimation is also presented via a non-parametric bootstrap approach. Simulation studies are performed to compare the estimations with and without constraints. Two real data sets are used to illustrate the proposed methods.
Persistent Identifierhttp://hdl.handle.net/10722/214578
ISSN
2019 Impact Factor: 1.186
2015 SCImago Journal Rankings: 1.283
ISI Accession Number ID

 

DC FieldValueLanguage
dc.contributor.authorDing, J-
dc.contributor.authorTian, GL-
dc.contributor.authorYuen, KC-
dc.date.accessioned2015-08-21T11:38:52Z-
dc.date.available2015-08-21T11:38:52Z-
dc.date.issued2015-
dc.identifier.citationComputational Statistics & Data Analysis, 2015, v. 84, p. 135-151-
dc.identifier.issn0167-9473-
dc.identifier.urihttp://hdl.handle.net/10722/214578-
dc.description.abstractThe constrained estimation in Cox’s model for the right-censored survival data is studied and the asymptotic properties of the constrained estimators are derived by using the Lagrangian method based on Karush–Kuhn–Tucker conditions. A novel minorization–maximization (MM) algorithm is developed for calculating the maximum likelihood estimates of the regression coefficients subject to box or linear inequality restrictions in the proportional hazards model. The first M-step of the proposed MM algorithm is to construct a surrogate function with a diagonal Hessian matrix, which can be reached by utilizing the convexity of the exponential function and the negative logarithm function. The second M-step is to maximize the surrogate function with a diagonal Hessian matrix subject to box constraints, which is equivalent to separately maximizing several one-dimensional concave functions with a lower bound and an upper bound constraint, resulting in an explicit solution via a median function. The ascent property of the proposed MM algorithm under constraints is theoretically justified. Standard error estimation is also presented via a non-parametric bootstrap approach. Simulation studies are performed to compare the estimations with and without constraints. Two real data sets are used to illustrate the proposed methods.-
dc.languageeng-
dc.publisherElsevier BV. The Journal's web site is located at http://www.elsevier.com/locate/csda-
dc.relation.ispartofComputational Statistics & Data Analysis-
dc.rights© 2015. This manuscript version is made available under the CC-BY-NC-ND 4.0 license http://creativecommons.org/licenses/by-nc-nd/4.0/-
dc.rightsThis work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.-
dc.subjectAsymptotic properties-
dc.subjectBootstrap approach-
dc.subjectConstrained estimation-
dc.subjectKarush-Kuhn-Tucker conditions-
dc.subjectMM algorithm-
dc.subjectProportional hazards model-
dc.titleA new MM algorithm for constrained estimation in the proportional hazards model-
dc.typeArticle-
dc.identifier.emailTian, GL: gltian@hku.hk-
dc.identifier.emailYuen, KC: kcyuen@hku.hk-
dc.identifier.authorityTian, GL=rp00789-
dc.identifier.authorityYuen, KC=rp00836-
dc.description.naturepostprint-
dc.identifier.doi10.1016/j.csda.2014.11.005-
dc.identifier.scopuseid_2-s2.0-84919650692-
dc.identifier.hkuros249987-
dc.identifier.volume84-
dc.identifier.spage135-
dc.identifier.epage151-
dc.identifier.isiWOS:000348263200010-
dc.publisher.placeNetherlands-
dc.identifier.issnl0167-9473-

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