By George A.F. Seber, Mohammad M. Salehi (auth.)
This booklet goals to supply an summary of a few adaptive suggestions utilized in estimating parameters for finite populations the place the sampling at any degree is dependent upon the sampling info received thus far. The pattern adapts to new details because it is available in. those equipment are particularly used for sparse and clustered populations.
Written by way of stated specialists within the box of adaptive sampling.
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Additional info for Adaptive Sampling Designs: Inference for Sparse and Clustered Populations
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13) takes the form of a stratified sample mean of a stratified random sample taken without replacement in which the variable of interest is whi . The stratum mean and variance for this variable are Wh = 1 Nh Nh whi and σh2 = i=1 1 Nh − 1 Nh (whi − W h )2 , i=1 and, from the stratified sampling theory (Sect. 4), 1 var[μHH,st ] = 2 N H Nh (Nh − n h ) h=1 σh2 . 14) An unbiased estimate of this variance is obtained by replacing σh2 by sh2 = 1 nh − 1 nh (whi − w h )2 . i=1 Other unbiased estimates are available including less efficient ones obtained by stopping the adaptive process at the stratum boundary or by not using any units added through crossing stratum boundaries.
G=1 To obtain similar results for the HH estimator we simply replace HT by HH in the above expressions to get μ H H,R B and its variance estimator. Substantial computations are required to obtain ξ and to compute expressions for each of the g combinations compatible with D R . More helpful formulae are needed. For example, Salehi (1999) introduced closed forms for both μ H H,R B and μ H T,R B along with unbiased estimators of their variances using the “inclusion–exclusion” formula which can be more readily computed.