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.