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A resampling variance estimator for the k nearest neighbours technique

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Abstract:

Current estimators of variance for the k nearest neighbours (kNN) technique are designed for estimates of population totals. Their efficiency in small-area estimation problems can be poor. In this study, we propose a modified balanced repeated replication estimator of variance (BRR) of a kNN total that performs well in small-area estimation problems and under both simple random and cluster sampling. The BRR estimate of variance is the sum of variances and covariances of unit-level kNN estimates in the area of interest. In Monte Carlo simulations of simple random and cluster sampling from seven artificial populations with real and simulated forest inventory data, the agreement between averages of BRR estimates of variance and Monte Carlo sampling variances was good both for population and for small-area totals. The modified BRR estimator is currently limited to sample sizes no larger than 1984. An accurate approximation to the proposed BRR estimator allows significant savings in computing time.

Les estimateurs courants de la variance pour la technique des k plus proches voisins (kPPV) ont été conçus pour estimer des totaux de population. Leur efficacité peut être faible dans le cas de problème d’estimation sur de petites superficies. Dans cette étude, nous proposons un estimateur modifié à réplication répétée et équilibrée (RRE) de la variance du total des kPPV qui est efficace pour des problèmes d’estimation sur de petites superficies et pour des échantillonnages aléatoires simples et en grappes. L’estimation RRE de la variance est la somme des variances et des covariances des estimations unitaires des kPPV dans la superficie visée. Dans des simulations de Monte Carlo d’échantillonnages aléatoires simples et en grappes à partir de sept populations artificielles comportant des données d’inventaire forestier réelles et simulées, les moyennes des estimations de la variance RRE correspondaient bien aux variances d’échantillonnage Monte Carlo pour les totaux de population et de petite superficie. La taille maximale de l’échantillon de l’estimateur modifié RRE est présentement de 1984. Une approximation juste de l’estimateur RRE proposé permet de réduire substantiellement le temps de calcul.

Document Type: Research Article

Publication date: April 1, 2010

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  • Published since 1971, this monthly journal features articles, reviews, notes and commentaries on all aspects of forest science, including biometrics and mensuration, conservation, disturbance, ecology, economics, entomology, fire, genetics, management, operations, pathology, physiology, policy, remote sensing, social science, soil, silviculture, wildlife and wood science, contributed by internationally respected scientists. It also publishes special issues dedicated to a topic of current interest.
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