Adjusting the bias of adaptive sampling estimators of spatial dispersion indexes by the δ-method
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It is common practice to investigate the spatial dispersion in a community of discrete individuals (like animals or plants). Usually, the study area is partitioned into spatial units of equal size and then the relationship between the first two moments of the variable representing the number of individuals in each plot is investigated. When the points are spread over a very wide area so that the population density is low but many points are concentrated inside a few units, then a suitable sample method for estimating the first two moments is adaptive sampling. However, since the more common dispersion indexes are non linear function of the first two moments, the resulting estimators are biased for finite samples. Accordingly, a procedure to adjust bias is required for small samples. In this paper a δ-method evaluation of the bias is proposed and the asymptotic distribution of the bias-corrected estimators is provided. Finally, a simulation study is performed in order to investigate the performance of the proposed procedure.
Key wordsSpatial dispersion indexes adaptive sampling bias reduction δ-method
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