Over the past few decades, major advances have taken place in both model-based and model-assisted approaches to inferences in finite population sampling. In the standard model-based approach, the finite population is assumed to be a realization from a superpopulation characterized by a probability distribution, and that the distribution of the sample is identical to that of the finite population. The model-based method could lead to a misleading inference if either assumption is violated. The model-assisted estimators typically are consistent or at least approximately unbiased with respect to the sampling design, and yet more efficient than the customary randomization-based estimators in the sense of achieving smaller variance with respect to the design if the assumed model is appropriate.

Since both approaches rely on the assumed model, there is a need to achieve robustness with respect to the model selection. This is precisely the main theme of this dissertation. This study uses the well-known Box-Cox transformation on the dependent variable to generate certain robust model-based and model-assisted estimators of finite population totals. The robustness is achieved since the appropriate transformation on the dependent variable is determined by the data. Both Monte Carlo simulation study and real data analyses are conducted to illustrate the robustness properties of the proposed estimation method using two different ways: (i) design-based, and (ii) model-based, wherever appropriate.

A few potential areas of future research within the context of transformations in linear regression models, as well as linear mixed models, for analysis of complex survey data are identified.