The estimation of a proportion in cluster sampling
Titel:
The estimation of a proportion in cluster sampling
Auteur:
Alalouf, I.S.
Verschenen in:
Communications in statistics
Paginering:
Jaargang 25 (1996) nr. 2 pagina's 325-343
Jaar:
1996
Inhoud:
In sampling with replacement with unequal probabilities, there are several natural estimators for the mean μy They are members of the class of so-called locurion-shift estimators, which are essentially Horvitz-Thompson estimators preceded by a shift in the location of each y by some quantity β. There is an optimal value for β , which in practice has to be replaced by an estimateβ. In large samples, this should cause no worry. But in small smples, the variability of β, and its correlation with other sample statistics, may cause serious biases or large mean square errors. It is difficult in general to evaluate the effect of substituting β for β because population characteristics are too wide-ranzing to allow for simple conclusions. But there is an important special case where a parameterized model can cover a reasonably wide range of populations, notably the case where y is a dichotomous variable and μy, is a proportion. π. We examine here by simulation five estimators of π in small to moderate samples
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