Sample-size-restrictive adaptive sampling: an application in estimating localized elements

In sample surveys sometimes one encounters a situation where, for many sampling units, one or more variables of interest are valued zero or negligibly low while for some other units they are substantial because of heavy localization of the high-valued units in certain segments. Estimation may then be inaccurate if a chosen sample fails to capture enough of the high-valued units. In such situations, adaptive sampling, as an extension of the initial sample to capture additional high-valued units, may be more serviceable. However, the size of an adaptive sample may often far exceed that of the initial sample. In this paper we present a method to put desirable constraints on the adaptive sample-size to keep the latter in check. To examine the efficacy of this method, we illustrate its application to estimate total numbers of rural earners through specific vocations in a given district in India simultaneously for several vocations.