Some asymptotic results for the systematic and stratified sampling of a finite population

A sample mean has an asymptotically insignificant model bias under a broad set of functional relationships between the parameter of interest and an auxiliary size variable given a systematic sample from a size ordered list. When based on randomly drawn samples within size strata, this estimator of the population mean not only has an asymptotically insignificant model bias but is design consistent as well. In addition, there are more efficient estimation strategies that have insignificant model biases and may be design consistent.