Regression-type estimators for adaptive two-stage sequential sampling

Adaptive two-stage sequential sampling (ATSSS) design was developed to observe more rare units and gain higher efficiency, in the sense of having a smaller variance estimator, than conventional sampling designs with equal effort for rare and spatially cluster populations. For certain rare populations, incorporating auxiliary variables into a sampling design can further improve the observation of rare units and increase efficiency. In this article, we develop regression-type estimators for ATSSS so that auxiliary variables can be incorporated into the ATSSS design when warranted. Simulation studies on two populations show that the regression-type estimators can significantly increase the efficiency of ATSSS and the detection of more rare units as compared to conventional sampling counterparts. Simulation of sampling of desert shrubs in Inner Mongolia (one of the two populations studied) showed that by incorporating a GIS auxiliary variable into ATSSS with the regression estimators resulted in a gain in efficiency over ATSSS without the auxiliary variable. Further, we found that the use of the GIS auxiliary variable in a conventional two-stage design with a regression estimator did not show a gain in efficiency.Acknowledgments We would like to thank two referees and an associate editor for their helpful suggestions on a previous draft of this article. The authors express their appreciation to the Ministry of Science and Technology and National Natural Sciences Foundation of China for fiscal support in the field work of Tamarix ramosissima population (Project Research Grants 31170588 and 2005DIB5JI42).Scopu

Asymptotic properties of the sample mean in adaptive stratified sequential sampling with multiple selection criteria

We extend the method of adaptive two-stage sequen-tial sampling to include designs where there is more than one crite-ria used in deciding on the allocation of additional sampling effort. These criteria, or conditions, can be a measure of the target popula-tion, or a measure of some related population. We develop Murthy estimator for the design that is unbiased estimators for the pop-ulation mean, and propose another, more efficient, estimator. We investigate asymptotic properties of this estimator. We use a sim-ulation study to investigate design properties of the multi-criteria adaptive stratified sequential sampling scheme and also some esti-mator properties under the design.Scopu