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Theory & Methods: Unbiased estimators for restricted adaptive cluster sampling
Author(s) -
Salehi Mohammad M.,
Seber George A.F.
Publication year - 2002
Publication title -
australian and new zealand journal of statistics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.434
H-Index - 41
eISSN - 1467-842X
pISSN - 1369-1473
DOI - 10.1111/1467-842x.00208
Subject(s) - estimator , mathematics , cluster sampling , statistics , minimum variance unbiased estimator , simple random sample , sampling (signal processing) , bias of an estimator , best linear unbiased prediction , sample size determination , variance (accounting) , population , computer science , selection (genetic algorithm) , demography , accounting , filter (signal processing) , artificial intelligence , sociology , business , computer vision
In adaptive cluster sampling the size of the final sample is random, thus creating design problems. To get round this, Brown (1994) and Brown & Manly (1998) proposed a modification of the method, placing a restriction on the size of the sample, and using standard but biased estimators for estimating the population mean. But in this paper a new unbiased estimator and an unbiased variance estimator are proposed, based on estimators proposed by Murthy (1957) and extended to sequential and adaptive sampling designs by Salehi & Seber (2001). The paper also considers a restricted version of the adaptive scheme of Salehi & Seber (1997a) in which the networks are selected without replacement, and obtains unbiased estimators. The method is demonstrated by a simple example. Using simulation from this example, the new estimators are shown to compare very favourably with the standard biased estimators.