In this thesis, we will investigate role of auxiliary variables in the both stages of designing and estimating unknown parameters of a population under adaptive designs, particularly adaptive two-stage sequential sampling. The role of auxiliary variable is first investigated in the design stage and we then use the auxiliary variable in the estimating stage for Regression and Ratio estimators. To construct Regression and Ratio estimators, we first assumed the mean of population for auxiliary variable is known. Eliminating this assumption, we then introduce a new design by incorporation Double sampling and Two-stage sequential sampling. Having fair comparisons among sampling designs, a cost function is introduced. Expected numbers of observed rare units are computed for adaptive and conventional designs. In order to strengthen adaptive designs, we extended Two-stage sequential sampling to include more than one condition. We develop a new efficient estimator for this design and its asymptotic properties will be investigated. Finally, the role of auxiliary variables in one the most efficient adaptive design will be investigated. Also some written “R” codes related to simulation in adaptive designs are presented as an appendix in the thesis.
