Modified whittle estimation of multilateral spatial models
We consider 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 difficulty of computing a continuous-frequency form of Whittle estimate or a time domain Gaussian maximum likelihood estimate, especially in case of multilateral models, due mainly to the Jacobian term. An extension of the discrete-frequency Whittle estimate from the time series literature deals conveniently with the latter 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. A Monte Carlo study of finite sample behaviour is included. The asymptotic regime allows increase in both directions, unlike the usual random fields formulation, with the central limit theorem established after re-ordering as a triangular array. When the data are non-Gaussian, the asymptotic variances of all parameter estimates are likely to be affected, and we provide a consistent, non-negative definite, estimate of the asymptotic variance matrix.
|Date of creation:||21 Nov 2003|
|Date of revision:|
|Contact details of provider:|| Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE|
Phone: (+44) 020 7291 4800
Fax: (+44) 020 7323 4780
Web page: http://cemmap.ifs.org.uk
More information through EDIRC
|Order Information:|| Postal: The Institute for Fiscal Studies 7 Ridgmount Street LONDON WC1E 7AE|
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Hannan, E. J. & Dunsmuir, W. T. M. & Deistler, M., 1980. "Estimation of vector ARMAX models," Journal of Multivariate Analysis, Elsevier, vol. 10(3), pages 275-295, September.
- Korezlioglu, Hayri & Loubaton, Philippe, 1986. "Spectral factorization of wide sense stationary processes on 2," Journal of Multivariate Analysis, Elsevier, vol. 19(1), pages 24-47, June.
- Robinson, Peter M, 1988. "The Stochastic Difference between Econometric Statistics," Econometrica, Econometric Society, vol. 56(3), pages 531-48, May.
When requesting a correction, please mention this item's handle: RePEc:ifs:cemmap:18/03. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Emma Hyman)
If references are entirely missing, you can add them using this form.