Parameter estimation of random fields with long-range dependence

This paper considers random fields with spectral density having a pole of fractional order at the origin. This class of models offers a suitable framework for studying long-range spatial correlation. An approximation to the likelihood function is given for the estimation of model parameters. The convergence rate of the approximation is obtained and an iterative method for maximising the approximate likelihood function is indicated. The method is applied to analyse a time series of maximum daily ozone levels and some texture data.