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For any one of these 1350 possibilities, 5000 samples were drawn from the example population concerned, using random sampling techniques appropriate to the method or estimator being considered, to yield 5000 estimates of the population mean, ( overline{Y} ), and its standard error, ( widehat{sigma}left overline{Y}right) ).
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There was little evidence of any appreciable bias with any of the methods or estimators or with any second-phase sample size.
There was no indication for any of the five examples or any of the methods or estimators that the level of bias was related to the target-auxiliary variable correlation level.
Figure 11 Scatter plots of the H s measured by the buoy and estimated by the standard method or proposed MLP-based estimators for the testing data set of the Ekofisk database.
Figure 13 Scatter plots of the H s measured by the buoy and estimated by the standard method or proposed MLP-based estimators for the training and validation data sets of the FINO 1 database.
Figure 15 Scatter plots of the H s measured by the buoy and estimated by the standard method or proposed MLP-based estimators for the testing data set of the FINO 1 database.
And second, there are still some H s underestimations, but they are lower in number than for the standard method and not predominant because the mean error of the H s estimate is close to 0 m. Figure 9 Scatter plots of the H s measured by the buoy and estimated by the standard method or proposed MLP-based estimators for the training and validation data sets of the Ekofisk database.
Since the size of the MLP does not vary in the experiments, the time needed for obtaining an estimate of the H s is the same as in the original case of study, i.e., ≈ 100 μs. Figure 17 Scatter plots of the H s measured by the buoy and estimated by the standard method or proposed MLP-based estimators for the testing data set of the Ekofisk database using the data set distribution of Figure 16.
The time for obtaining an estimate of the H s is the same as in the original case and as for the other platform, i.e., ≈ 100 μs. Figure 19 Scatter plots of significant wave heights measured by the buoy and estimated by the standard method or proposed MLP-based estimators for the testing data set of the FINO 1 database using the data set distribution of Figure 18.
Mathematically, the wave telescope method or the minimum variance estimator is regarded as the maximum likelihood method assuming a Gaussian shape for the likelihood function.
Building on Imbens (2000), Hirano and Imbens (2004) developed a generalization of the binary treatment propensity score and labeled the method a GPS estimator or propensity score with continuous treatments.
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