Canadian Forest Service Publications

A new mean squared error estimator for a synthetic domain mean. 2017. Magnussen, S. For. Sci. 63(1):1–9

Year: 2017

Issued by: Pacific Forestry Centre

Catalog ID: 39004

Language: English

Availability: PDF (request by e-mail)

Available from the Journal's Web site.
DOI: 10.5849/forsci.16-056

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Mark record


Model-based predictions of a domain (stand) mean of a study variable Y is synthetic when there are no direct observations of Y within the domain of interest. In the absence of estimators of domain effects in a model used for domain-level predictions, the use of model-based estimators of variance can lead to overly narrow confidence intervals with poor coverage and a serious underestimation of uncertainty. This study proposes a new mean squared error estimator (MSE4) based on an estimator of the among-domain variance in Y derived with fitted values of yˆ. In simulated sampling, with at most one sample taken from a domain, 95% confidence intervals based on MSE4 provided better, yet unsatisfactory, coverage than possible with available alternatives. A shift to sampling designs affording estimators of domain effects is recommended.

Plain Language Summary

Enhanced forest inventories (EFI) are now using population models derived from a sample to predict a stand-level variable of interest (say stem volume). If the model does not include stand-effects because the sampling design disallows their estimation, the obtained stand mean has an unknown amount of bias and an unknown variance. This problem is largely ignored and the uncertainty in a stand estimate is (naively) obtained with a textbook estimator for a population mean. To improve this situation a new ‘stop-gap’ estimator of uncertainty is developed. It is superior to three previously proposed estimators. The worst estimator is the often used textbook estimator. It is concluded that the best way forward is a paradigm shift in the inventory design to include replicated sampling within a subset of stands in order to estimate stand effects. Lacking data of this kind, the new estimator of uncertainty is currently the best available alternative to a naïve application of a textbook estimator for a population mean.