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Likelihood-based confidence bands for fault lines in response surfaces

Hall, Peter; Rau, Christian

Description

We consider the problem of constructing asymptotic confidence bands, both pointwise and simultaneous, for a smooth fault line in a response surface when the design is represented by a point process, either deterministic or stochastic, with intensity n diverging to infinity. The estimator of the fault line is defined as the ridge line on the likelihood surface which arises from locally fitting a model that employs a linear approximation to the fault line, to a kernel smooth of the data. The...[Show more]

dc.contributor.authorHall, Peter
dc.contributor.authorRau, Christian
dc.date.accessioned2015-12-13T22:19:20Z
dc.identifier.issn0178-8051
dc.identifier.urihttp://hdl.handle.net/1885/71741
dc.description.abstractWe consider the problem of constructing asymptotic confidence bands, both pointwise and simultaneous, for a smooth fault line in a response surface when the design is represented by a point process, either deterministic or stochastic, with intensity n diverging to infinity. The estimator of the fault line is defined as the ridge line on the likelihood surface which arises from locally fitting a model that employs a linear approximation to the fault line, to a kernel smooth of the data. The construction is based on analysis of the limiting behaviour of perpendicular distance from a point on the true fault line to the nearest point on the ridge. We derive asymptotic properties of bias, and the limiting distribution of stochastic error. This distribution is given by the location of the maximum of a Gaussian process with quadratic drift. Although the majority of attention is focused on the regression problem, the limiting distribution is shown to have wider relevance to local-likelihood approaches to fault line estimation for density or intensity surfaces.
dc.publisherSpringer
dc.sourceProbability Theory and Related Fields
dc.subjectKeywords: Boundary estimation; Change point; Edge detection; Frontier analysis; Gaussian process with quadratic drift; Image analysis; Jump; Kernel methods; Least squares; Locally parametric methods; Multivariate confidence bands; Response surface; Smoothing
dc.titleLikelihood-based confidence bands for fault lines in response surfaces
dc.typeJournal article
local.description.notesImported from ARIES
local.description.refereedYes
local.identifier.citationvolume124
dc.date.issued2002
local.identifier.absfor010405 - Statistical Theory
local.identifier.ariespublicationMigratedxPub2857
local.type.statusPublished Version
local.contributor.affiliationHall, Peter, College of Physical and Mathematical Sciences, ANU
local.contributor.affiliationRau, Christian, College of Physical and Mathematical Sciences, ANU
local.description.embargo2037-12-31
local.bibliographicCitation.startpage26
local.bibliographicCitation.lastpage49
local.identifier.doi10.1007/s004400100195
dc.date.updated2015-12-11T07:46:30Z
local.identifier.scopusID2-s2.0-0036026178
CollectionsANU Research Publications

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