By George A.F. Seber, Mohammad M. Salehi (auth.)
This ebook goals to supply an summary of a few adaptive concepts utilized in estimating parameters for finite populations the place the sampling at any degree is dependent upon the sampling details got up to now. The pattern adapts to new info because it is available in. those tools are specially used for sparse and clustered populations.
Written through stated specialists within the box of adaptive sampling.
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Extra info for Adaptive Sampling Designs: Inference for Sparse and Clustered Populations
2000. ” Survey Methodology 26:87–98. F. Seber. 1994. ” Biometrics 50:712–724. F. Seber. 1996. Adaptive Sampling. New York: Wiley. Woodby, D. 1998. ” Proceedings of the North Pacific Symposium on Invertebrate Stock Assessment and Management 125:15–20. Canadian special publication of fisheries and aquatic sciences. , C. Kleinn, L. Fehrmann, S. Tang, and S. Magnussen. 2011. A New Design for Sampling with Adaptive Sample Plots. Environmental and Ecological Statistics 18:223–237. , Z. Zhu, and B. Hu.
If bk is the number of times network k is intersected by the initial sample of primary networks, we can also use the HH estimator from Eq. 17), namely K 1 MN μHH = k=1 1 Mn1 = yk∗ K k=1 bk , E[bk ] bk yk∗ , xk since bk has the hypergeometric distribution with parameters (N , xk , n 1 ) and mean n 1 xk /N . We note that n1 bk = Jik , i=1 where Jik = 1 if the ith primary unit intersects the kth network, and 0 otherwise. 4) κi k=1 yk∗ , xk and κi is the number of networks that intersect the ith primary unit.
Applying the above theory to networks rather than units we have that for any adaptive sampling scheme, D R is a minimal sufficient statistic for (y1∗ , y2∗ , . . , y K∗ ). Since μ M is not a function of d R as it does not use any of the (ν − n) edge units added adaptively and not selected in the initial sample, we can use the Rao-Blackwell theorem to improve on our estimate as follows. Suppose there are h edge units in the final sample, that is in d R , then h − (ν − n) of these are initially selected as networks of size one not satisfying the condition C and are successively “removed” from the population, but are later found to be among the edge units of the initially selected clusters.