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.

引用

页码：261 / 267

页数：7

共 50 条

[41] AN EMPIRICAL EVALUATION OF THE ACCURACY OF THE HARTLEY AND RAO (1962) VARIANCE APPROXIMATION FOLLOWING PPS SYSTEMATIC SAMPLING
Gregoire, Timothy G.
Li, Zhimin
[J]. PAKISTAN JOURNAL OF STATISTICS, 2011, 27 (04): : 555 - 566
[42] The Use of Calibration Weighting for Variance Estimation Under Systematic Sampling: Applications to Forest Cover Assessment
Fattorini, Lorenzo
Gregoire, Timothy G.
Trentini, Sara
[J]. JOURNAL OF AGRICULTURAL BIOLOGICAL AND ENVIRONMENTAL STATISTICS, 2018, 23 (03) : 358 - 373
[43] Systematic study on the variability in the gasoline sampling process at service stations and its contribution to the measurement variance
Gonzalez-Hernandez, Jerson
Fuentes-Schweizer, Paola
[J]. ACCREDITATION AND QUALITY ASSURANCE, 2024, 29 (01) : 31 - 36
[44] Systematic study on the variability in the gasoline sampling process at service stations and its contribution to the measurement variance
Jerson González-Hernández
Paola Fuentes-Schweizer
[J]. Accreditation and Quality Assurance, 2024, 29 : 31 - 36
[45] Comparison of estimators of variance for forest inventories with systematic sampling-results from artificial populations
Magnussen, Steen
McRoberts, Ronald E.
Breidenbach, Johannes
Nord-Larsen, Thomas
Stahl, Goran
Fehrmann, Lutz
Schnell, Sebastian
[J]. FOREST ECOSYSTEMS, 2020, 7 (01)
[46] Systematic Alias Sampling: An Efficient and Low-Variance Way to Sample from a Discrete Distribution
Vallivaara, Ilari
Poikselka, Katja
Rikula, Pauli
Roning, Juha
[J]. ACM TRANSACTIONS ON MATHEMATICAL SOFTWARE, 2017, 43 (03):
[47] Comparison of estimators of variance for forest inventories with systematic sampling-results from artificial populations
Steen Magnussen
Ronald E.McRoberts
Johannes Breidenbach
Thomas Nord-Larsen
G?ran St?hl
Lutz Fehrmann
Sebastian Schnell
[J]. Forest Ecosystems, 2020, 7 (02) : 215 - 233
[48] Finite-population variance estimation under systematic sampling schemes with multiple random starts
Sampath, S.
Ammani, S.
[J]. JOURNAL OF STATISTICAL COMPUTATION AND SIMULATION, 2012, 82 (08) : 1207 - 1221
[49] The Use of Calibration Weighting for Variance Estimation Under Systematic Sampling: Applications to Forest Cover Assessment
Lorenzo Fattorini
Timothy G. Gregoire
Sara Trentini
[J]. Journal of Agricultural, Biological and Environmental Statistics, 2018, 23 : 358 - 373
[50] Preferential sampling of helicity by isotropic helicoids
Gustavsson, Kristian
Biferale, Luca
[J]. PHYSICAL REVIEW FLUIDS, 2016, 1 (05):

← 1 2 3 4 5 →