Parameter estimates for fractional autoregressive spatial processes

Y. Boissy; B. B. Bhattacharyya; X. Li; G. D. Richardson

doi:10.1214/009053605000000589

paper

Parameter estimates for fractional autoregressive spatial processes

arXiv:math/0501423 · doi:10.1214/009053605000000589

Abstract

A binomial-type operator on a stationary Gaussian process is introduced in order to model long memory in the spatial context. Consistent estimators of model parameters are demonstrated. In particular, it is shown that $d^_{N} - d = O_{P} (\frac{( Log N ) ^{3}}{N})$ , where $d = (d_{1}, d_{2})$ denotes the long memory parameter.

Published at http://dx.doi.org/10.1214/009053605000000589 in the Annals of Statistics (http://www.imstat.org/aos/) by the Institute of Mathematical Statistics (http://www.imstat.org)