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The matrices so obtained are the reduced-rank approximation of the sample correlation matrices.
Another alternative to sample permutation testing that addresses the key challenge of computational complexity is the parametric approximation of the sample permutation distribution of gene-level score statistics developed by Zhou et al. [ 34].
Competitive gene set testing methods that correctly account for correlation among gene-level test statistics, either through sample permutation, parametric approximation of the sample permutation distribution or correlation adjustment of parametric test statistics, include SAFE [ 31, 33, 34], GSEA [ 35], GSA [ 36] and CAMERA [ 32].
The limit of quantification (LOQ) was calculated as three times the ILOD amount for each compound (Tables 2 and 3), by approximation of the sample volume to 100 μL and of the lipids to be 20 mg extracted from 5 g plasma.
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The former was evaluated based on a constant rectangular approximation of the sampled data and impulse response function in a number of steps corresponding to the sampling rate, while the latter interpolates the sampled data in an arbitrary number of sub-steps and then integrates over the sub-steps and steps.
Using this approximation, the determinant of the information matrix, and therefore the approximation of the sampling variance of heritability, can be negative, when n > (1 − t)/(h × var(r ij)).
To obtain a better approximation of the sampled counterpart model to the real stochastic structure of the demand, it would be desirable to apply variance reduction techniques such as Importance Sampling, and to switch to a variable-sample approach which allows the consideration of a much larger set of random scenarios without compromising runtime too much.
The method only needs one slightly-off-axis interferogram to extract the phase distribution with no offline measurements and approximations of the sample or the reference fields required.
20, 21 For each of these countries we used a normal approximation of the sampling distribution of the sample proportion.
In this paper, we discuss different approximation methods in the estimation of the sample mean and standard deviation and propose some new estimation methods to improve the existing literature.
For the problem of limited sample size, Escobar and Meeker [44] used the Monte Carlo (MC) method to simulate the implementation of the optimal plan based on the asymptotic variance, calculate the sample variance of the pth quantile, and investigate the applicability of the theoretical optimal plan by the approximation degree of the sample variance and asymptotic variance.
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