Statistical analysis of ratio estimators and their estimators of variances when the auxiliary variate is measured with error
 Christian Salas,
 Timothy G. Gregoire
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Forest inventory relies heavily on sampling strategies. Ratio estimators use information of an auxiliary variable (x) to improve the estimation of a parameter of a target variable (y). We evaluated the effect of measurement error (ME) in the auxiliary variate on the statistical performance of three ratio estimators of the target parameter total τ_{ y }. The analyzed estimators are: the ratioofmeans, meanofratios, and an unbiased ratio estimator. Monte Carlo simulations were conducted over a population of more than 14,000 loblolly pine (Pinus taeda L.) trees, using tree volume (v) and diameter at breast height (d) as the target and auxiliary variables, respectively. In each simulation three different sample sizes were randomly selected. Based on the simulations, the effect of different types (systematic and random) and levels (low to high) of MEs in x on the bias, variance, and mean square error of three ratio estimators was assessed. We also assessed the estimators of the variance of the ratio estimators. The ratioofmeans estimator had the smallest root mean square error. The meanofratios estimator was found quite biased (20%). When the MEs are random, neither the accuracy (i.e. bias) of any of the ratio estimators is greatly affected by type and level of ME nor its precision (i.e. variance). Positive systematic MEs decrease the bias but increase the variance of all the ratio estimators. Only the variance estimator of the ratioofmeans estimator is biased, being especially large for the smallest sample size, and larger for negative MEs, mainly if they are systematic.
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 Title
 Statistical analysis of ratio estimators and their estimators of variances when the auxiliary variate is measured with error
 Journal

European Journal of Forest Research
Volume 129, Issue 5 , pp 847861
 Cover Date
 20100901
 DOI
 10.1007/s1034200902773
 Print ISSN
 16124669
 Online ISSN
 16124677
 Publisher
 SpringerVerlag
 Additional Links
 Topics
 Keywords

 Sampling
 Forest inventory
 Designbased inference
 Variance estimators
 Bias
 Authors

 Christian Salas ^{(1)} ^{(2)}
 Timothy G. Gregoire ^{(1)}
 Author Affiliations

 1. School of Forestry and Environmental Studies, Yale University, 360 Prospect Street, New Haven, CT, 065112104, USA
 2. Departamento de Ciencias Forestales, Universidad de La Frontera, Temuco, Chile