Equation (3.5) yields the same estimates of Theorem 4.2.4 in the book [21].
The purpose of this note is to point out a simple modification to the analyses of variance which yields the same estimates as REML for many of the designs commonly used in ecological studies.
Finally, maximum likelihood analyses of the concatenated datasets using a variety of substitution models (JTT, MTREV, WAG, RTREV, CPREV, VT) consistently yielded the same estimates, which completely corroborate the trees generated by Bayesian inference and MP analyses of the concatenated datasets (Additional file 8).
It is demonstrated that the estimates produced by the designed sliding-mode mean-square filter and the Kalman Bucy filter yield the same estimation-error variance.
The method yields the same estimate of the failure probability as the simple Monte Carlo, with a computational cost limited to the evaluation of a subset of the selected samples.
We must note that this resulting estimate of the TDI yields the same estimate as that directly computed from equation (2) using the sample counterparts, however as we will illustrate in subsequent sections this binary search algorithm is necessary to compute our proposal for the upper confidence limit of TDI.
The results displayed in Figure 1 demonstrate that, when there is no imbalance at baseline (i.e. Z T ′ − Z C ′ = 0 ), all three statistical methods yield the same unbiased estimate of treatment effect, irrespective of the level of ZY correlation or the standardized effect size.
The analysis of childhood height yielded relatively the same estimates of SNP-heritability for cross-platform imputed GRMs, suggesting a slight increase of the estimate in comparison to the combined GRM.
RMLA and its approximation RRWA yielded the same effect estimates, and estimating the marker effects with RRWA took less than 1 sec for medium-sized data sets (Table 2).
Obviously, the images of the same test set as shown in the individual columns in Fig. 2 should within reasonable error estimates yield the same lattice parameters and derived results because these images possess the same translation symmetry per design.
