Model-based nonparametric variance estimation for systematic sampling in a forestry survey

Systematic sampling is frequently used in natural resource and other 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 describe a new 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 the consistency of the estimator for both the anticipated variance and the design variance. We compare the nonparametric variance estimators with several design-based estimators on data from a forestry survey.