Constrained Inverse Adaptive Cluster Sampling

In adaptive cluster sampling, first proposed by Thompson (1990, 1992) and studied in detail by Thompson and Seber (1996), an initial sample of units is selected and, whenever the value of the variable of interest satisfies a specified condition, neighbouring units are added to the sample. The neighbourhood of a unit may be defined by spatial proximity or, in the case of human population, by social or genetic links or other connections. One problem that has not yet studied deeply enough is the possibility that no units that satisfy the condition for extra sampling are selected in the initial sample. When this happens the adaptive cluster sampling would coincide with the initial sample and no information would be gathered on the study variable. To avoid this drawback in this paper we introduce a new adaptive cluster design denominated constrained inverse adaptive cluster sampling (CIAC) and whose aim is to ensure the presence in the initial sample of at least one unit satisfying the condition for extra sampling. This aim is hold by a sequential selection of the initial sample. This sort of selection of the initial units, explained in detail in the next section, introduces a bias into the estimators of the mean of the population usually used in the adaptive cluster sampling. To overcome this difficulty two new unbiased estimators of the mean of the population are suggested in the paper.