Asymptotics in adaptive cluster sampling

Environmental and Ecological Statistics - Tập 10 - Trang 61-82 - 2003
MARTÍN H. FÉLIX-MEDINA1
1Escuela de Ciencias Físico Matemáticas, Universidad Autónoma de Sinaloa, Ciudad Universitaria, Culiacán Sinaloa

Tóm tắt

In this article we consider asymptotic properties of the Horvitz-Thompson and Hansen-Hurwitz types of estimators under the adaptive cluster sampling variants obtained by selecting the initial sample by simple random sampling without replacement and by unequal probability sampling with replacement. We develop an asymptotic framework, which basically assumes that the number of units in the initial sample, as well as the number of units and networks in the population tend to infinity, but that the network sizes are bounded. Using this framework we prove that under each of the two variants of adaptive sampling above mentioned, both the Horvitz-Thompson and Hansen-Hurwitz types of estimators are design-consistent and asymptotically normally distributed. In addition we show that the ordinary estimators of their variances are also design-consistent estimators.

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Environmental and Ecological Statistics

Tập 10

61-82

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