2014/05/20 by Rao, Suhasini Subba
#FOS: Mathematics #Statistics Theory (math.ST)
paper · doi:10.48550/arxiv.1405.5240
A class of Fourier based statistics for irregular spaced spatial data is introduced, examples include, the Whittle likelihood, a parametric estimator of the covariance function based on the L2-contrast function and a simple nonparametric estimator of the spatial autocovariance which is a non-negative function. The Fourier based statistic is a quadratic form of a discrete Fourier-type transform of the spatial data. Evaluation of the statistic is computationally tractable, requiring O(nb) operations, where b are the number Fourier frequencies used in the definition of the statistic and n is the sample size. The asymptotic sampling properties of the statistic are derived using both increasing domain and fixed domain spatial asymptotics. These results are used to construct a statistic which is asymptotically pivotal.