Efficiency of Some Sampling Designs for Spatially Clustered Populations

Abstract

SUMMARYThe eciencies of two sampling designs for estimating the mean of a ®xed, ®nite population are considered. The ®rst is adaptive cluster sampling (ASRS; Thompson, 1990 Journal of the American Statistical Association) which is designed to adaptively increase sampling eort in the neighbourhood of units whose observed value meets some prede®ned condition. The other is Balanced Sampling Excluding Contiguous Units (BSEC) (Hedayat, Rao and Stufken, 1988, Journal of Statistical Planning and Inference), a conventional design in which neighbouring units are deliberately excluded from being sampled under the idea that they provide little new information to the sampling eort. We consider the eect of type of neighbourhood, initial sample size, condition for adaptively sampling neighbours, and degree and extent of clustering in the population on the eciency of ASRS relative to BSEC and simple random sampling. Populations having dierent degrees of clustering are simulated using a modi®ed Neyman±Scott process. We compare the design-based variances of two estimators, a Horvitz±Thompson-type estimator and a Hansen±Hurwitz-type estimator. While the Horvitz±Thompson-type estimator can have the lowest variance under some of the situations explored, it is also the most sensitive to changes in the conditions. The eciency of the estimator often comes at the cost of a large eective sample size. In general, ASRS is more ecient when the population elements are rare and highly clustered although BSEC designs are generally more ecient for a wider array of combinations of conditions.

Occupancy estimation for rare species using a spatially‐adaptive sampling design

“…A separate area of expansion involves the exploration of various neighbourhood structures. Christman () found physically contiguous neighbourhoods to be most efficient for classical adaptive sampling and this may be relevant as well. Additionally, we believe these models could be valuable in non‐adaptive sampling approaches also.…”

A review of adaptive cluster sampling: 1990?2003

“…The results of Smith et al (1995) suggest that the magnitude of the within-network variance relative to the total population variance may be the most important factor determining efficiency. Christman (1996bChristman ( , 1997 verified computationally that b l HH performs well relative to y from an SRS when the within-network variance is a high proportion of the total variance and a first-order neighborhood is used. Similar results were noted for b l HT .…”

“…As with the choice of a critical value, if the surveyor had prior knowledge of the population structure, then the efficiency of ACS using b l HH can be increased by selecting the unit size accordingly Christman (1996bChristman ( , 1997. These results were corroborated by the simulation study of Smith et al (1995) that compared the efficiency of several designs using Horvitz-Thompson estimation to estimate s for several species of wintering waterfowl.…”

Adaptive cluster sampling for estimation of deforestation rates

“…Under favorable circumstances, ACS can be very efficient in terms of precision and cost. Practical experience with ACS remains scant and the results so far indicate that both design effects and costs can be highly variable (Lo et al 1997;Brown and Manly 1998;Ringvall 2000;Christman 2002;Hanselman et al 2003;Smith et al 2003;Brown 2003). Modifications of ACS aimed at capping the number of units sampled, by, for example, introducing a stopping rule or by optimizing the adaptive protocol, do not appear to have achieved gains of practical importance (Mohammad and Seber 1997;Lo et al 1997;Christman and Lan 2001;Su and Quinn 2003).…”