By George A.F. Seber, Mohammad M. Salehi (auth.)
This ebook goals to supply an summary of a few adaptive strategies utilized in estimating parameters for finite populations the place the sampling at any level is dependent upon the sampling details acquired to this point. The pattern adapts to new details because it is available in. those equipment are specifically 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
1 Overlapping Strata Suppose the total population of N units is partitioned into H strata, with Nh units in the hth stratum (h = 1, 2, . . , H ). Define unit (h, i) to be the ith unit in the hth stratum with associated y-value yhi . A simple random sample of n h units is taken H n h is the initial total sample size. Further from the hth stratum so that n 0 = h=1 units are added adaptively without regard to stratum boundaries. Ignoring the edge units, we then have the usual HT estimator [cf. 5 Stratified Adaptive Cluster Sampling μHT ,st = 45 yk∗ Jk , αk K 1 NT k=1 with αk , the probability of intersecting network k with initial samples in each of the strata, is now given by H αk = 1 − h=1 Nh − xhk nk Nh nh , where xhk is the number of units in stratum h that lie in network k.
Chapter 5 Inverse Sampling Methods Abstract Inverse sampling is an adaptive method whereby it is the sample size that is adaptive. On the basis of a new proof, Murthy’s estimator can now be applied with or without adaptive cluster sampling to inverse sampling to provide unbiased estimators of the mean and variance of the mean estimator. A number of sequential plans along with parameter estimates are considered including a general inverse sampling design, multiple inverse sampling when subpopulation sizes are known, quota sampling, multiple inverse sampling, and truncated multiple inverse sampling.
3) with the basic sampling unit now being the network (with yi replaced by yi∗ ). An unbiased estimate of μ is therefore μM = 1 N n yi∗ i=1 P(s R | i) , P(s R ) where P(s R | i) denotes the conditional probability of getting sample s R , given the ith network was selected first, s R is the unordered sample of n networks, and P(s R | i) is the probability of choosing sample s R given network i has been chosen as the first network. Now if pi is the probability of getting network i in the first draw, we have pi = xi /N .