Canadian Forest Service Publications

In search of a variance estimator for systematic sampling. 2019. Magnussen, S., Fehrmann, L. Scandinavian Journal of Forest Research, 34:4, pp. 300-312.

Year: 2019

Issued by: Pacific Forestry Centre

Catalog ID: 40120

Language: English

Availability: PDF (request by e-mail)

Available from the Journal's Web site.
DOI: 10.1080/02827581.2019.1599063

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Mark record


Seven variance estimators to be used under systematic sampling are evaluated in a simulation study with 270 artificial spatial populations with different levels and structure of autocorrelation. In settings without an auxiliary variable a proposed new spatial resampling estimator RHO is recommended. In setting with an auxiliary variable, an estimator based on post-stratification (PST), and one with a correction for spatial autocorrelation (DOR), generated estimates with less bias than the SRS estimator in the majority of studied settings. Only in populations with either a near zero autocorrelation at the interval of sampling, or a very strong correlation between the target and the auxiliary variable did the otherwise conservative SRS estimator perform as well as the alternatives.

Plain Language Summary

National forest inventories employs a form of systematic sampling to obtain a spatially balanced sample. Unfortunately there is no design-unbiased estimator of variance for systematic sampling. A quasi default estimator in use by practice is the estimator for simple random sampling (SRS). This estimator typically inflates the variance, hence underestimates precision. The degree of overestimation depends on the spatial autocorrelation structure in the population In a simulation study with replicated systematic sampling from 270 artificial populations with different levels and structures of spatial autocorrelation we found that two estimators, as a rule, generated less biased estimates than SRS. A proposed new estimator of variance, although the least biased in a majority of settings, it was also prone to underestimate the variance in settings with an auxiliary variable and a strong spatial autoregressive process. Our key finding is that we have alternative estimators of variance (ready to be used) that will perform much better than the quasi default SRS estimator of variance when data comes from systematic sampling. This is important since the SRS estimator of variance may cast a NFI design as less efficient and precision as lower than it actually is.