0518662 - FGÚ 2020 RIV SI eng J - Článek v odborném periodiku
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
Grant CEP: GA MŠMT(CZ) LM2015062; GA MŠMT(CZ) EF16_013/0001775; GA ČR(CZ) GAP302/12/1207
Výzkumná infrastruktura: Czech-BioImaging - 90062
Institucionální podpora: RVO:67985823
Klíčová slova: isotropic design * spatial statistics * stereology * systematic sampling * variance
Obor OECD: Applied mathematics
Impakt faktor: 0.550, rok: 2019 ; AIS: 0.28, rok: 2019
Způsob publikování: Open access
Web výsledku:
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.
Trvalý link: http://hdl.handle.net/11104/0303749