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Abstract:
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We provide an elementary derivation of Kadane (2005)'s dynamic sampling plan by first directly finding the sample allocation that minimizes a decomposed weighted objective function, similar to (Wright, 2017). We then prove that the sample allocation also minimizes the sampling variance, as is also done by Kadane.
In the context of sampling sequentially from a stratified population where sampling costs vary among the strata, the plan specifies from which stratum to take the next sample unit which reduces variance by the largest amount per unit cost. Whenever sampling stops, the realized allocation minimizes the sampling variance for the cost C* at that point, as well as for any cost and allocation that costs less than C*. Our derivation and proof provide complete insight into why Kadane's plan works.
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