VARIANCE OF THE ISOTROPIC UNIFORM SYSTEMATIC SAMPLING

被引：0
|
作者：
Janacek, Jiri [1 ]
Jirak, Daniel [2 ,3 ]
机构：
[1] Czech Acad Sci, Inst Physiol, Dept Biomath, Videnska 1083, Prague 14220, Czech Republic
[2] Inst Clin & Expt Med, Dept Diagnost & Intervent Radiol, MR Unit, Videnska 1958-9, Prague 14021, Czech Republic
[3] Charles Univ Prague, Fac Med 1, Inst Biophys & Informat, Prague, Czech Republic
来源：
IMAGE ANALYSIS & STEREOLOGY | 2019年 / 38卷 / 03期
关键词：
isotropic design; spatial statistic; stereology; systematic samplings; variance;
D O I：
10.5566/ias.2218
中图分类号：
T [工业技术];
学科分类号：
08 ;
摘要：
The integral of a smooth function with bounded support over a set with finite perimeter in Euclidean space R-d 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.
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页码：261 / 267
页数：7
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