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Optimal PPS Sampling with Vanishing Auxiliary Variables – with Applications in Microscopy

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  • Ina Trolle Andersen
  • Ute Hahn
  • Eva B. Vedel Jensen

Abstract

type="main" xml:id="sjos12156-abs-0001"> Recently, non-uniform sampling has been suggested in microscopy to increase efficiency. More precisely, proportional to size (PPS) sampling has been introduced, where the probability of sampling a unit in the population is proportional to the value of an auxiliary variable. In the microscopy application, the sampling units are fields of view, and the auxiliary variables are easily observed approximations to the variables of interest. Unfortunately, often some auxiliary variables vanish, that is, are zero-valued. Consequently, part of the population is inaccessible in PPS sampling. We propose a modification of the design based on a stratification idea, for which an optimal solution can be found, using a model-assisted approach. The new optimal design also applies to the case where ‘vanish’ refers to missing auxiliary variables and has independent interest in sampling theory. We verify robustness of the new approach by numerical results, and we use real data to illustrate the applicability.

Suggested Citation

  • Ina Trolle Andersen & Ute Hahn & Eva B. Vedel Jensen, 2015. "Optimal PPS Sampling with Vanishing Auxiliary Variables – with Applications in Microscopy," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 42(4), pages 1136-1148, December.
    • Handle: RePEc:bla:scjsta:v:42:y:2015:i:4:p:1136-1148
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    File URL: http://hdl.handle.net/10.1111/sjos.12156
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    References listed on IDEAS

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    1. Linda V. Hansen & Markus Kiderlen & Eva B. Vedel Jensen, 2011. "Image‐Based Empirical Importance Sampling: An Efficient Way of Estimating Intensities," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 38(3), pages 393-408, September.
    2. Desislava Nedyalkova & Yves Tillé, 2008. "Optimal sampling and estimation strategies under the linear model," Biometrika, Biometrika Trust, vol. 95(3), pages 521-537.
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