Systematic sampling with errors in sample locations
Systematic sampling of points in continuous space is widely used in microscopy and spatial surveys. Classical theory provides asymptotic expressions for the variance of estimators based on systematic sampling as the grid spacing decreases. However, the classical theory assumes that the sample grid i...
| Main Authors: | , , , |
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| Format: | Journal Article |
| Published: |
Oxford University Press
2010
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| Online Access: | http://hdl.handle.net/20.500.11937/42701 |
| _version_ | 1848756492657754112 |
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| author | Ziegel, J. Baddeley, Adrian Dorph-Petersen, K. Jensen, E. |
| author_facet | Ziegel, J. Baddeley, Adrian Dorph-Petersen, K. Jensen, E. |
| author_sort | Ziegel, J. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Systematic sampling of points in continuous space is widely used in microscopy and spatial surveys. Classical theory provides asymptotic expressions for the variance of estimators based on systematic sampling as the grid spacing decreases. However, the classical theory assumes that the sample grid is exactly periodic; real physical sampling procedures may introduce errors in the placement of the sample points. This paper studies the effect of errors in sample positioning on the variance of estimators in the case of one-dimensional systematic sampling. First we sketch a general approach to variance analysis using point process methods. We then analyze three different models for the error process, calculate exact expressions for the variances, and derive asymptotic variances. Errors in the placement of sample points can lead to substantial inflation of the variance, dampening of zitterbewegung, that is fluctuation effects, and a slower order of convergence. This suggests that the current practice in some areas of microscopy may be based on over-optimistic predictions of estimator accuracy. © 2010 Biometrika Trust. |
| first_indexed | 2025-11-14T09:13:04Z |
| format | Journal Article |
| id | curtin-20.500.11937-42701 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T09:13:04Z |
| publishDate | 2010 |
| publisher | Oxford University Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-427012018-03-29T09:07:45Z Systematic sampling with errors in sample locations Ziegel, J. Baddeley, Adrian Dorph-Petersen, K. Jensen, E. Systematic sampling of points in continuous space is widely used in microscopy and spatial surveys. Classical theory provides asymptotic expressions for the variance of estimators based on systematic sampling as the grid spacing decreases. However, the classical theory assumes that the sample grid is exactly periodic; real physical sampling procedures may introduce errors in the placement of the sample points. This paper studies the effect of errors in sample positioning on the variance of estimators in the case of one-dimensional systematic sampling. First we sketch a general approach to variance analysis using point process methods. We then analyze three different models for the error process, calculate exact expressions for the variances, and derive asymptotic variances. Errors in the placement of sample points can lead to substantial inflation of the variance, dampening of zitterbewegung, that is fluctuation effects, and a slower order of convergence. This suggests that the current practice in some areas of microscopy may be based on over-optimistic predictions of estimator accuracy. © 2010 Biometrika Trust. 2010 Journal Article http://hdl.handle.net/20.500.11937/42701 10.1093/biomet/asp067 Oxford University Press restricted |
| spellingShingle | Ziegel, J. Baddeley, Adrian Dorph-Petersen, K. Jensen, E. Systematic sampling with errors in sample locations |
| title | Systematic sampling with errors in sample locations |
| title_full | Systematic sampling with errors in sample locations |
| title_fullStr | Systematic sampling with errors in sample locations |
| title_full_unstemmed | Systematic sampling with errors in sample locations |
| title_short | Systematic sampling with errors in sample locations |
| title_sort | systematic sampling with errors in sample locations |
| url | http://hdl.handle.net/20.500.11937/42701 |