By George A.F. Seber, Mohammad M. Salehi (auth.)

This booklet goals to supply an outline of a few adaptive ideas utilized in estimating parameters for finite populations the place the sampling at any level will depend on the sampling details bought up to now. The pattern adapts to new info because it is available in. those tools are particularly used for sparse and clustered populations.

Written by means of stated specialists within the box of adaptive sampling.

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**Additional resources for Adaptive Sampling Designs: Inference for Sparse and Clustered Populations**

**Example text**

It is therefore sensible to look at an intermediate solution. Dryver and Thompson (2005) derived two easy-to-compute estimators of higher efficiency than their corresponding original estimators μ H T and μ H T by taking the expected value of the usual estimators conditional on a sufficient statistic that is not minimally sufficient. 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.

E. +1) unit ensures that any pair of units has a positive probability of being included in the initial sample. The latter requirement is needed for unbiased variance estimation. It essentially combines the features of a systematic sample with additional random sampling and allows for unbiased estimation of the variance using a HT estimator. It can be regarded as a type of “space-filling” design. For some details and examples see Thompson (1991a) and Thompson and Seber (1996, pp. 128–134). There are two major restrictions for the simple Latin square design +1: (i) populations units must be arranged in a square and (ii) the sample size must be N + 1 from a population of size N 2 .

1) 30 3 Rao-Blackwell Modifications Let ν denote the number of distinct units in the final adaptive sample, and define G = nν1 , the number of possible combinations or “groups” of n 1 distinct units from the ν in the sample. Suppose these combinations are indexed in an arbitrary way by the label g (g = 1, 2, . . , G). Let tg be the value of T when the initial sample consists of combination g, and let var g [T ] denote the value of the unbiased estimator var[T ] when computed using the gth combination.