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Nonparametric estimation of hazard rate under the constraint of monotonicity

Hall, Peter; Gijbels, I; Gifford, J; Huang, Li-ling

Description

This article shows how to smoothly "monotonize" standard kernel estimators of hazard rate, using bootstrap weights. Our method takes a variety of forms, depending on choice of kernel estimator and on the distance function used to define a certain constrained optimization problem. We confine attention to a particularly simple kernel approach and explore a range of distance functions. It is straightforward to reduce "quadratic" inequality constraints to "linear" equality constraints, and so our...[Show more]

dc.contributor.authorHall, Peter
dc.contributor.authorGijbels, I
dc.contributor.authorGifford, J
dc.contributor.authorHuang, Li-ling
dc.date.accessioned2015-12-13T23:27:00Z
dc.identifier.issn1061-8600
dc.identifier.urihttp://hdl.handle.net/1885/93105
dc.description.abstractThis article shows how to smoothly "monotonize" standard kernel estimators of hazard rate, using bootstrap weights. Our method takes a variety of forms, depending on choice of kernel estimator and on the distance function used to define a certain constrained optimization problem. We confine attention to a particularly simple kernel approach and explore a range of distance functions. It is straightforward to reduce "quadratic" inequality constraints to "linear" equality constraints, and so our method may be implemented using little more than conventional Newton-Raphson iteration. Thus, the necessary computational techniques are very familiar to statisticians. We show both numerically and theoretically that monotonicity, in either direction, can generally be imposed on a kernel hazard rate estimator regardless of the monotonicity or otherwise of the true hazard rate. The case of censored data is easily accommodated. Our methods have straightforward extension to the problem of testing for monotonicity of hazard rate, where the distance function plays the role of a test statistic.
dc.publisherAmerican Statistical Association
dc.sourceJournal of Computational and Graphical Statistics
dc.subjectKeywords: Bandwidth; Biased bootstrap; Censored data; Decreasing hazard rate; Increasing hazard rate; Power divergence; Survival analysis
dc.titleNonparametric estimation of hazard rate under the constraint of monotonicity
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume10
dc.date.issued2001
local.identifier.absfor010405 - Statistical Theory
local.identifier.ariespublicationMigratedxPub26438
local.type.statusPublished Version
local.contributor.affiliationHall, Peter, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationGijbels, I, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationGifford, J, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationHuang, Li-ling, College of Asia and the Pacific, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.startpage592
local.bibliographicCitation.lastpage614
dc.date.updated2015-12-12T09:48:37Z
local.identifier.scopusID2-s2.0-0035628555
CollectionsANU Research Publications

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