0518662 - FGÚ 2020 RIV SI eng J - Journal Article
Janáček, Jiří - Jirák, D.
Variance of the isotropic uniform systematic sampling.
Image Analysis and Stereology. Roč. 38, č. 3 (2019), s. 261-267. ISSN 1580-3139
R&D Projects: GA MŠMT(CZ) LM2015062; GA MŠMT(CZ) EF16_013/0001775; GA ČR(CZ) GAP302/12/1207
Research Infrastructure: Czech-BioImaging - 90062
Institutional support: RVO:67985823
Keywords : isotropic design * spatial statistics * stereology * systematic sampling * variance
OECD category: Applied mathematics
Impact factor: 0.550, year: 2019 ; AIS: 0.28, rok: 2019
Method of publishing: Open access
Result website:
https://ias-iss.org/ojs/IAS/article/view/2218DOI: https://doi.org/10.5566/ias.2218

The integral of a smooth function with bounded support over a set with finite perimeter in Euclidean space ℝd is estimated using a periodic grid in an isotropic uniform random position. Extension term in the estimator variance is proportional to the integral of the squared modulus of the function over the object boundary and to the grid scaling factor raised to the power of d+1. Our result generalizes the Kendall-Hlawka-Matheron formula for the variance of the isotropic uniform systematic estimator of volume.
Permanent Link: http://hdl.handle.net/11104/0303749