Alternative mean-squared error estimators for synthetic estimators of domain means

S. Magnussen, G. Frazer and M. Penner

Journal of Applied Statistics, 2016, vol. 43, issue 14, 2550-2573

Abstract: In forest management surveys, the mean of a variable of interest (Y) in a population composed of N equal area spatial compact elements is increasingly estimated from a model linking Y to an auxiliary vector X known for all elements in the population. It is also desired to have synthetic estimates of the mean of Y in spatially compact domains (forest stands) with no or at most one sample-based observation of Y. We develop three alternative estimators of mean-squared errors (MSE) that reduce the risk of a serious underestimation of the uncertainty in a synthetic estimate of a domain mean in cases where the employed model does not accounts for domain effects nor spatial autocorrelation in unobserved residual errors. Expansions of the estimators including anticipated effects of a spatial autocorrelation in residual errors are also provided. Simulation results indicate that the conventional model-dependent (MD) population-level estimator of variance in a synthetic estimate of a domain mean underestimates uncertainty by a wide margin. Our alternative estimators mitigated, in settings with weak to moderate domain effects and relatively small sample sizes, to a large extent, the problem of underestimating uncertainty. We demonstrate applications with examples from two actual forest inventories.

Date: 2016
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DOI: 10.1080/02664763.2016.1142942

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