AJOR  Vol.2 No.1 , March 2012
Optimizing Forest Sampling by Using Lagrange Multipliers
ABSTRACT
In two-phase sampling, or double sampling, from a population with size N we take one, relatively large, sample size n. From this relatively large sample we take a small sub-sample size m, which usually costs more per sample unit than the first one. In double sampling with regression estimators, the sample of the first phase n is used for the estimation of the average of an auxiliary variable X, which should be strongly related to the main variable Y (which is estimated from the sub-sample m). Sampling optimization can be achieved by minimizing cost C with fixed var Y, or by finding a minimum var Y for fixed C. In this paper we optimize sampling with use of Lagrange multipliers, either by minimizing variance of Y and having predetermined cost, or by minimizing cost and having predetermined variance of Y.

Cite this paper
K. Kitikidou, "Optimizing Forest Sampling by Using Lagrange Multipliers," American Journal of Operations Research, Vol. 2 No. 1, 2012, pp. 94-99. doi: 10.4236/ajor.2012.21011.
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