Modified Whittle estimation of multilateral models on a lattice

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dc.contributor.author Robinson, P.M.
dc.contributor.author Vidal-Sanz, Jose M.
dc.date.accessioned 2010-04-12T14:44:00Z
dc.date.available 2010-04-12T14:44:00Z
dc.date.issued 2006
dc.identifier.bibliographicCitation Journal of Multivariate Analysis, 2006, 97, 5, p. 1090–1120
dc.identifier.issn 0047-259X
dc.identifier.uri http://hdl.handle.net/10016/7249
dc.description.abstract In the estimation of parametric models for stationary spatial or spatio-temporal data on a d-dimensional lattice, for d≥2, the achievement of asymptotic efficiency under Gaussianity, and asymptotic normality more generally, with standard convergence rate, faces two obstacles. One is the “edge effect”, which worsens with increasing d. The other is the possible difficulty of computing a continuous-frequency form of Whittle estimate or a time domain Gaussian maximum likelihood estimate, due mainly to the Jacobian term. This is especially a problem in “multilateral” models, which are naturally expressed in terms of lagged values in both directions for one or more of the d dimensions. An extension of the discrete-frequency Whittle estimate from the time series literature deals conveniently with the computational problem, but when subjected to a standard device for avoiding the edge effect has disastrous asymptotic performance, along with finite sample numerical drawbacks, the objective function lacking a minimum-distance interpretation and losing any global convexity properties. We overcome these problems by first optimizing a standard, guaranteed non-negative, discrete-frequency, Whittle function, without edge-effect correction, providing an estimate with a slow convergence rate, then improving this by a sequence of computationally convenient approximate Newton iterations using a modified, almost-unbiased periodogram, the desired asymptotic properties being achieved after finitely many steps. The asymptotic regime allows increase in both directions of all d dimensions, with the central limit theorem established after re-ordering as a triangular array. However our work offers something new for “unilateral” models also. When the data are non-Gaussian, asymptotic variances of all parameter estimates may be affected, and we propose consistent, non-negative definite estimates of the asymptotic variance matrix.
dc.format.mimetype application/pdf
dc.format.mimetype text/plain
dc.language.iso eng
dc.publisher Elsevier
dc.rights ©Elsevier
dc.subject.other Spatial data
dc.subject.other Multilateral modelling
dc.subject.other Whittle estimation
dc.subject.other Edge effect
dc.subject.other Consistent variance estimation
dc.title Modified Whittle estimation of multilateral models on a lattice
dc.type article
dc.type.review PeerReviewed
dc.description.status Publicado
dc.relation.publisherversion http://dx.doi.org/10.1016/j.jmva.2005.05.013
dc.subject.eciencia Empresa
dc.identifier.doi 10.1016/j.jmva.2005.05.013
dc.rights.accessRights openAccess
dc.identifier.publicationfirstpage 1090
dc.identifier.publicationissue 5
dc.identifier.publicationlastpage 1120
dc.identifier.publicationtitle Journal of Multivariate Analysis
dc.identifier.publicationvolume 97
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