By George A.F. Seber, Mohammad M. Salehi (auth.)
This ebook goals to supply an outline of a few adaptive thoughts utilized in estimating parameters for finite populations the place the sampling at any degree is dependent upon the sampling details received so far. The pattern adapts to new info because it is available in. those tools are specially used for sparse and clustered populations.
Written via stated specialists within the box of adaptive sampling.
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Extra info for Adaptive Sampling Designs: Inference for Sparse and Clustered Populations
9)] αirs = αir + αis − 1 − Ni − xir − xis ni Ni ni . 4 Two-Stage Adaptive Cluster Sampling 43 Also, from Eq. 2), Ki Ki Vi = var[τi ] = αirs − αir αis αir αs yir∗ yis∗ r =1 s=1 . 9) i=1 M τi . 11) i=1 αirs − αir αis αirs αir αis . 12) Here κi is the number of distinct networks intersected in primary unit i. As the distinct unordered units and their labels form a minimal sufficient statistic for any adaptive sampling scheme, the Rao-Blackwell theorem can be used to provide unbiased estimators with smaller variances.
They incorporated only those edge units that were in the initial sample. Deriving Rao-Blackwell versions of the HT and HH estimators of a ratio (see Salehi 2001) or of the ratio estimators (see Dryver and Chao 2007) for ACS is much more complicated. Chao et al. (2011) noted that the approaches used by Salehi (1999) and Felix-Medina (2000) do not provide simplified analytical forms of their RaoBlackwellized versions. They proposed four alternative improved ratio estimators in which the Rao-Blackwellization technique is utilized in a straightforward manner.
If n i = 2, then it is shown in Appendix 3 of Salehi and Seber (1997) that Vi is always nonnegative. Finally we note that Rocco (2008) proposed a restricted version of two-stage adaptive cluster sampling, adopting a similar approach to Salehi and Seber (2002). 9) is generally negligible (Särndal et al. 1992, p. 139) and var[μ1 ] < v, where v=E 2 M 2sM N T2 m . Suppose that a pilot survey has been run in which a sample of size m 0 PSUs has been chosen and the n i are selected according to the same rules to be used for the 2 but full survey being planned.