Optimal PPS Sampling with Vanishing Auxiliary Variables – with Applications in Microscopy. (5th May 2015)

• Record Type: Journal Article
• Authors: Andersen, Ina Trolle; Hahn, Ute; Vedel Jensen, Eva B.
• Is Part Of: Scandinavian journal of statistics. Volume 42:Number 4(2015:Dec.)
• Page Start: 1136
• Page End: 1148
• Publication Date: 2015-05-05
• Subjects: Horvitz–Thompson estimator -- microscopy -- model‐assisted sampling -- optimal allocation -- proportional regression models -- systematic PPS sampling -- vanishing auxiliary variables; Statistics -- Periodicals; 310
• DOI: 10.1111/sjos.12156
• Languages: English
• ISSNs: 0303-6898

Abstract

Abstract: 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.