Find in Library
Search millions of books, articles, and more
Indexed Open Access Databases
Variance of the Isotropic Uniform Systematic Sampling
oleh: Jiri Janacek, Daniel Jirak
Format: | Article |
---|---|
Diterbitkan: | Slovenian Society for Stereology and Quantitative Image Analysis 2019-12-01 |
Deskripsi
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.