The Annals of Statistics

Parameter estimates for fractional autoregressive spatial processes

Y. Boissy, B. B. Bhattacharyya, X. Li, and G. D. Richardson

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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 $\hat{d}_{N}-d=O_{P}(\frac{(\operatorname{Log}N)^{3}}{N})$, where d=(d1,d2) denotes the long memory parameter.

Article information

Source
Ann. Statist., Volume 33, Number 6 (2005), 2553-2567.

Dates
First available in Project Euclid: 17 February 2006

Permanent link to this document
https://projecteuclid.org/euclid.aos/1140191666

Digital Object Identifier
doi:10.1214/009053605000000589

Mathematical Reviews number (MathSciNet)
MR2253095

Zentralblatt MATH identifier
1085.62107

Subjects
Primary: 62F12: Asymptotic properties of estimators 62M30: Spatial processes

Keywords
Parameter estimation autoregressive spatial process spectral density function long memory

Citation

Boissy, Y.; Bhattacharyya, B. B.; Li, X.; Richardson, G. D. Parameter estimates for fractional autoregressive spatial processes. Ann. Statist. 33 (2005), no. 6, 2553--2567. doi:10.1214/009053605000000589. https://projecteuclid.org/euclid.aos/1140191666


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