Adaptive cluster sampling is a design specifically developed for rare and clustered populations. Using this sampling design, we consider the case when an auxiliary variable is available in addition to the variable of interest. The use of auxiliary information has been shown to improve the efficiency of estimators although this results in asymptotically design-unbiased estimators. Consider wildlife population in a protected area. Its distribution and abundance can partly be influenced by such factors as disease and pollution where the presence of wildlife diseases or higher environmental pollution decreases population totals and the distribution of wildlife. This paper proposes two product estimators and their associated variance estimators for the adaptive cluster sampling design to be used when the study and auxiliary variables are negatively correlated. The exact expression of the bias together with the mean square error to the first degree of approximation has been obtained. We derived the conditions under which the proposed estimators provided a more accurate estimation than the Horvitz–Thompson and Hansen–Hurwitz estimators with adaptive cluster sampling and the product estimator with simple random sampling. A simulation study was carried out to show the performance of the proposed estimators. Moreover, theoretical findings were supported by a numerical example using real data.

Adaptive cluster sampling for negatively correlated data

GATTONE, Stefano Antonio;
2016-01-01

Abstract

Adaptive cluster sampling is a design specifically developed for rare and clustered populations. Using this sampling design, we consider the case when an auxiliary variable is available in addition to the variable of interest. The use of auxiliary information has been shown to improve the efficiency of estimators although this results in asymptotically design-unbiased estimators. Consider wildlife population in a protected area. Its distribution and abundance can partly be influenced by such factors as disease and pollution where the presence of wildlife diseases or higher environmental pollution decreases population totals and the distribution of wildlife. This paper proposes two product estimators and their associated variance estimators for the adaptive cluster sampling design to be used when the study and auxiliary variables are negatively correlated. The exact expression of the bias together with the mean square error to the first degree of approximation has been obtained. We derived the conditions under which the proposed estimators provided a more accurate estimation than the Horvitz–Thompson and Hansen–Hurwitz estimators with adaptive cluster sampling and the product estimator with simple random sampling. A simulation study was carried out to show the performance of the proposed estimators. Moreover, theoretical findings were supported by a numerical example using real data.
File in questo prodotto:
File Dimensione Formato  
env2381.pdf

Solo gestori archivio

Tipologia: PDF editoriale
Dimensione 246.95 kB
Formato Adobe PDF
246.95 kB Adobe PDF   Visualizza/Apri   Richiedi una copia
product_environmetrics.pdf

accesso aperto

Tipologia: Documento in Pre-print
Dimensione 277.39 kB
Formato Adobe PDF
277.39 kB Adobe PDF Visualizza/Apri

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11564/654027
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus 15
  • ???jsp.display-item.citation.isi??? ND
social impact