Parameter estimates for fractional autoregressive spatial processes

Details Parameter estimates for fractional autoregressive spatial processes Parameter estimates for fractional autoregressive spatial processes

2005-01-24

arxiv.org/abs/math/0501423v2

Annals of Statistics 2005, Vol. 33, No. 6, 2553-2567

Mathematics

Statistics Theory

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

Scientific paper

10.1214/009053605000000589

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
$\hat{d}_N-d=O_P(\frac{(\operatorname {Log}N)^3}{N})$, where $d=(d_1,d_2)$
denotes the long memory parameter.

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