Systematic sampling is a frequently used sampling method in natural resource surveys, because of its ease of implementation and its design efficiency. An important drawback of systematic sampling, however, is that no direct estimator of the design variance is available. We propose an estimator of the model-based expectation of the design variance, under a nonparametric model for the population. The nonparametric model is sufficiently flexible that it can be expected to hold at least approximately for many practical situations. We prove that the nonparametric variance estimator is both a consistent estimator for the model-based expectation of the design variance and a consistent predictor for the design variance in the model-based context. This variance estimator's properties are further explored through a simulation study. An application in Forest Inventory and Analysis (FIA) is discussed in the second chapter. We compare the nonparametric variance estimator with the variance estimators for random stratified sampling and simple random sampling. The nonparametric variance estimator performs very well and it also has the advantage of allowing more complex models. A discussion about selecting proper auxiliary variables is also carried out for this application. In the last chapter, we study model averaging in survey estimation. Model averaging is a widely used method as it accounts for uncertainties in model selection. However, its applications in survey estimation are yet to be explored. We propose a model-averaging (MA) regression estimator for the population total. The goal is to provide a method that will work well for a wide range of response variables and situations. Different ways to obtain this estimator are explored through large-scale simulation studies.