ADAPTIVE CLUSTER SAMPLING BASED ON ORDER STATISTICS

Abstract

In adaptive cluster sampling designs, neighbouring units are added to the sample whenever the value of the variable of interest satisfies a chosen criterion. Commonly, the criterion consists of a fixed, prespecified value, so that additional units are added to the sample whenever a unit is observed exceeding that prespecified value. In some surveys it may be difficult to pick an appropriate fixed value ahead of time. In such cases, the criterion for additional sampling may be made relative to the observed sample values by basing it on the sample order statistics. For example, in an environmental survey, concentrations of a pollutant are measured at each site in an initial sample of 100 sites. Additional sites are then added to the sample in the neighbourhoods of the top 10 sites, that is, those sites with the ten largest order statistics of the variable of interest. If any of the added sites also have large values, still more sites may be added to the sample. With the criterion based on sample order statistics, the situation differs mathematically from that of ordinary adaptive cluster sampling since the network associations of units vary from sample to sample. Biases thus arise in conventional estimators of the population mean or total; as well as in estimators which are unbiased under adaptive cluster sampling with fixed criteria. In this paper, unbiased estimators and estimators of variance are given for adaptive cluster sampling based on order statistics.