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    Systematic sampling with errors in sample locations

    Access Status
    Fulltext not available
    Authors
    Ziegel, J.
    Baddeley, Adrian
    Dorph-Petersen, K.
    Jensen, E.
    Date
    2010
    Type
    Journal Article
    
    Metadata
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    Citation
    Ziegel, J. and Baddeley, A. and Dorph-Petersen, K. and Jensen, E. 2010. Systematic sampling with errors in sample locations. Biometrika. 97 (1): pp. 1-13.
    Source Title
    Biometrika
    DOI
    10.1093/biomet/asp067
    ISSN
    0006-3444
    School
    Department of Mathematics and Statistics
    URI
    http://hdl.handle.net/20.500.11937/42701
    Collection
    • Curtin Research Publications
    Abstract

    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.

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