Optimizing Forest Sampling by Using Lagrange Multipliers

Kyriaki Kitikidou

Department of Forestry and Management of the Environment and Natural Resources, Democritus University of Thrace, Orestiada, Greece.

DOI: 10.4236/ajor.2012.21011                

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.

Keywords

Forest Inventories; Lagrange Multipliers; Optimization, Sampling

Conflicts of Interest

The authors declare no conflicts of interest.

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