Geodesic
Adjusted Euler--MacLaurin predictor for
Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 3, pp. 596-608

Voir la notice de l'article provenant de la source Math-Net.Ru

We consider the problem of predicting integrals of a spatial stationary process $Z$ over a unit square. We construct predictors based on a systematic sampling of size $m^2$ by approximating the existing mean squared derivatives of the process in the two-dimensional Euler–MacLaurin formula by finite differences up to some appropriate order. We show that if the spectral density satisfies $f_{Z}(\omega) =o(|\omega|^{-p})$ for any fixed positive integer $p$, the corresponding mean squared error is of order $m^{-p}$.
Keywords: spatial stationary process, predictor, Euler–MacLaurin formula. 
@article{TVP_2003_48_3_a10,
     author = {K. Benhenni and R. Drouilhet},
     title = {Adjusted {Euler--MacLaurin} predictor for},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {596--608},
     publisher = {mathdoc},
     volume = {48},
     number = {3},
     year = {2003},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TVP_2003_48_3_a10/}
}
TY  - JOUR
AU  - K. Benhenni
AU  - R. Drouilhet
TI  - Adjusted Euler--MacLaurin predictor for
JO  - Teoriâ veroâtnostej i ee primeneniâ
PY  - 2003
SP  - 596
EP  - 608
VL  - 48
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TVP_2003_48_3_a10/
LA  - en
ID  - TVP_2003_48_3_a10
ER  - 
%0 Journal Article
%A K. Benhenni
%A R. Drouilhet
%T Adjusted Euler--MacLaurin predictor for
%J Teoriâ veroâtnostej i ee primeneniâ
%D 2003
%P 596-608
%V 48
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TVP_2003_48_3_a10/
%G en
%F TVP_2003_48_3_a10
K. Benhenni; R. Drouilhet. Adjusted Euler--MacLaurin predictor for. Teoriâ veroâtnostej i ee primeneniâ, Tome 48 (2003) no. 3, pp. 596-608. http://geodesic.mathdoc.fr/item/TVP_2003_48_3_a10/