Remote sensing to reduce the effects of spatial autocorrelation on design-based inference for forest inventory using systematic samples

Systematic sampling is often used to select plot locations for forest inventory estimation. However, it is not possible to derive a design-unbiased variance estimator for a systematic sample using one random start. As a result, many forest inventory analysts resort to applying variance estimators that are design-unbiased following simple random sampling to their systematic samples even though this typically leads to conservative estimates of error. We explore the influence of spatial autocorrelation on variance estimation when systematic sampling is employed using repeated sampling. We generate a sequence of 1000 synthetic populations with increasing spatial autocorrelation and repeatedly sample from each to examine how the performance of estimators change as spatial autocorrelation changes. We also repeatedly sample from a tree census plot in Harvard Forest, Massachusetts and examine the performance of similar estimators. Results indicate that applying variance estimators that are unbiased following simple random sampling to systematic samples from populations exhibiting stronger spatial autocorrelation tend to be more conservative. We also find that incorporating ancillary wall-to-wall covariates, e.g., remote sensing data, using generalized regression estimators can reduce variance over-estimation by explaining some or all of the spatial structure in the population.