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T. Gregoire, “Roots of Forest inventory in North America,” A Paper Presented at the A1 Inventory Working Group Session at the SAF National Convention Held at Richmond, VA, 25-28 October 1992.

has been cited by the following article:

• TITLE: Optimizing Forest Sampling by Using Lagrange Multipliers

  AUTHORS: Kyriaki Kitikidou

  KEYWORDS: Forest Inventories; Lagrange Multipliers; Optimization, Sampling

  JOURNAL NAME: American Journal of Operations Research, Vol.2 No.1, March 14, 2012

  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.