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Optimizing Forest Sampling by Using Lagrange Multipliers

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Author(s): Kyriaki Kitikidou

Journal: American Journal of Operations Research
ISSN 2160-8830

Volume: 02;
Issue: 01;
Start page: 94;
Date: 2012;
Original page

Keywords: Forest Inventories; Lagrange Multipliers; Optimization | Sampling

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.

Tango Jona
Tangokurs Rapperswil-Jona

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