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Alternative mean-squared error estimators for synthetic estimators of domain means. (English) Zbl 07281635
Summary: 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 $$\mathbf{X}$$ 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.
##### MSC:
 62 Statistics
nlmdl
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