: In many sample surveys, the population appears to be rare and/or geographically clustered. Such populations are frequently found in ecology, biology and environmental sciences. In such situations, the adaptive sampling designs are usually more efficient than conventional designs. However, the resulted unbiased estimators have often highly skewed distributions. This is the case where the normal approximation-based confidence intervals based on small samples may lead to unsatisfactory results, with poor coverage properties. In this thesis we investigate the nonparametric approaches to set confidence intervals for the population mean under two famous types of adaptive sampling; inverse sampling and adaptive cluster sampling. We develop the idea of the bootstrap and empirical likelihood methods to mentioned sampling designs and compare the efficiency of those with the normal approximation method.