ISSN:
1572-9311
Keywords:
efficient estimator
;
empirical estimator
;
Gibbs fields
;
local interactions
;
random field
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract The expectation of a local function on a stationary random field can be estimated from observations in a large window by the empirical estimator, that is, the average of the function over all shifts within the window. Under appropriate conditions, the estimator is consistent and asymptotically normal. Suppose that the field is a Gibbs field with known finite range of interactions but otherwise unknown potential. We show that the empirical estimator is efficient if and only if the function is (equivalent to) a sum of functions each of which depends only on the values of the field on a clique of sites.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1023/A:1009993904851
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