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The estimates of the sample covariance matrix and the M-estimator do not require this assumption and are, in general, not diagonal matrices.
First we illustrate the effectiveness of the two sample eigenvalue density estimation methods: We show that the polynomial method makes good estimates of the sample eigenvalue densities if the number of population eigenvalue clusters is low, but fails if that number increases.
Figure 7a shows the estimates of the sample eigenvalue distribution for the first setting.
Right panel: scatter plot estimates of the sample size required to reach 80% statistical power as a function of the CV in K i.
Person and item separation indexes were also considered; these indexes are estimates of the sample's spread relative to the precision (SE) of those measurements.
Estimates of the sample haplotype frequencies together with their standard deviation, a list of the most likely pairs of haplotypes for each individual together with their probability, and the estimates of recombination parameters in the region, were calculated using the same software under the assumption of a stepwise mutation mechanism for multiallelic loci.
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IT-based model averaging allows the estimation of confidence intervals that incorporate model estimates of the sampling variance for each model and of the model selection uncertainty.
The covariance matrix is obtained by adding the matrix with design-based estimates of the sampling variances and covariances and the covariance matrix of the model errors.
Although auto-correlation will lead to biased estimates of the sampling variance of the effect size, meta-analysis of response ratios can be conducted with robust variance estimation procedures that remain valid even when sampling variance estimates are biased.
We obtain empirical Bayes estimates of the sample-specific overall mutation rates q j (by assigning the prior distribution of q j to be Uniform a, b) and estimating the posterior mean).
When L is fixed, although estimates of the sample-specific dropout rates γ i⋅ are not affected by the value of N, our estimates of the locus-specific dropout rates γ⋅ℓ and the inbreeding coefficient ρ become closer to the true values as N increases.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com