Hence, the model was over-simplified, assuming that V (θ, τ, M) depended weakly on parameters and could be replaced by a constant matrix, based on its sample estimate.
where is average symbol energy and has been replaced by its sample average estimate.
Under the assumption that the neighboring pixels have the identical terrain height and the complex reflectivity is independent from pixel-to-pixel [16], the weight covariance matrix C js (i w) given by (16) can be estimated by its sample covariance matrix C ^ js i, w, i.e., C ^ js i, w = 1 2 K + 1 ∑ k = − K K js i + k, w j s H i + k, w (17).
In their place, the measures of uncertainty output by SEATS for its finite-sample estimates are measures for semi-infinite data estimates, used as approximations.
As with expansion estimators in survey estimation [ 15], weighing each observation by its inverse sampling fraction, roughly, yields an estimate of the number of individuals representative of the "study base" [ 16].
Sample estimates were verified by bootstrapping.
In ideal circumstances, such a-priori hypotheses would be accompanied by a sample size estimate specific for testing moderators.
Yet unless the training sample is collected by probability sampling, the estimates are, at best, of uncertain quality, and may be substantially biased.
We assessed this effect by simulating Poisson sampling of estimated rates.
