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Variance of the isotropic uniform systematic sampling

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    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 MŠk(CZ) LM2015062; GA MŠk(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
    Subject RIV: BD - Theory of Information
    OBOR OECD: Applied mathematics
    Impact factor: 0.550, year: 2019
    https://ias-iss.org/ojs/IAS/article/view/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

     
     
Number of the records: 1