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Modified whittle estimation of multilateral models on a lattice

Robinson, Peter M. and Vidal Sanz, J. (2005) Modified whittle estimation of multilateral models on a lattice. EM/05/492. Suntory and Toyota International Centres for Economics and Related Disciplines, London School of Economics and Political Science, London, UK.

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Identification Number: EM/05/492

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 reordering 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.

Item Type: Monograph (Discussion Paper)
Official URL: http://sticerd.lse.ac.uk
Additional Information: © 2005 Peter M Robinson and J Vidal Sanz
Subjects: H Social Sciences > HB Economic Theory
Sets: Collections > Economists Online
Departments > Economics
Research centres and groups > Suntory and Toyota International Centres for Economics and Related Disciplines (STICERD)
Date Deposited: 28 Apr 2008 17:08
Last Modified: 01 Oct 2010 08:52
URI: http://eprints.lse.ac.uk/id/eprint/4545

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