Model-Assisted Estimation of a Spatial Population Mean

This paper deals with the estimation of the mean of a spatial population. Under a design-based approach to inference, an estimator assisted by a penalized spline regression model is proposed and studied. Proof that the estimator is design-consistent and has a normal limiting distribution is provided...

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Bibliographic Details
Published in:International statistical review 2012-04, Vol.80 (1), p.111-126
Main Authors: Cicchitelli, Giuseppe, Montanari, Giorgio E.
Format: Article
Language:English
Subjects:
Confidence intervals
Consistent estimators
Estimation methods
Estimators
Estimators for the mean
Horvitz-Thompson estimation
model-assisted estimator
Population estimates
Population mean
Random sampling
Regression analysis
Sampling
sampling design
Simulation
Spatial models
Spline regression model
Statistical variance
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Summary:This paper deals with the estimation of the mean of a spatial population. Under a design-based approach to inference, an estimator assisted by a penalized spline regression model is proposed and studied. Proof that the estimator is design-consistent and has a normal limiting distribution is provided. A simulation study is carried out to investigate the performance of the new estimator and its variance estimator, in terms of relative bias, efficiency, and confidence interval coverage rate. The results show that gains in efficiency over standard estimators in classical sampling theory may be impressive. Cet article traite de l'estimation de la moyenne d'une population spatiale. Dans le cadre d'une approche fondée sur un plan d'échantillonnage, un estimateur assisté par un modle de régression spline pénalisé est proposé et étudié. Nous montrons que cet estimateur est convergent (dans le cadre du plan) et établissons sa loi normale asymptotique. Une étude de simulation est menée afin d'étudier ses performances et l'estimation de sa variance, ainsi que les questions liées au biais relatif, à l'efficacité, et au taux de convergence des probabilités de couverture des intervalles de confiance correspondants. Ces simulations indiquent des gains d'efficacité considérables par rapport aux estimateurs découlant des méthodes d'échantillonnage classiques.
ISSN:0306-7734
1751-5823
DOI:10.1111/j.1751-5823.2011.00164.x