TY - JOUR
T1 - Systematic sampling with errors in sample locations
AU - Ziegel, Johanna
AU - Baddeley, Adrian
AU - Dorph-Petersen, Karl-Anton
AU - Jensen, Eva Bjørn Vedel
N1 - Preprint available on http://www.imf.au.dk/publs?id=681
PY - 2010
Y1 - 2010
N2 - 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.
AB - 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.
U2 - 10.1093/biomet/asp067
DO - 10.1093/biomet/asp067
M3 - Journal article
SN - 0006-3444
VL - 97
SP - 1
EP - 13
JO - Biometrika
JF - Biometrika
IS - 1
ER -