The p values are based on large sample approximations, and these are less valid when events are sparse.
We adopt L = 2048 as the filter order, l = L/8 = 256 sampling columns for the Column-Sampling approximation and the Nyström method, and an extra l = L/4 = 512 sampling number for the latter.
Figure 3 For different numbers of samples ( l ), cosines of principal angles between the exact and the approximated eigenvectors obtained by the Column-Sampling approximation and the Nyström method, respectively.
Two optimization algorithms, one based on large-sample approximation, and the other based on Monte Carlo simulation, are developed to find the optimal plans.
Bold font marks cases where the value of the Anderson-Darling statistic A 2 is smaller than the critical level A 0.05 2 = 2.492 (large-sample approximation) and the hypothesis of two datasets being sampled from the same distribution can not be rejected at a 5% significance level.
One possible reason is that the real scenario more RFIs exists, the Notch filtering method is so inflexible that makes more frequency gaps, and as shown in Figure 6d, f, the Column-Sampling approximation and the Nyström method with 512 samples still have the similar suppression effects.
From these we produce analytic finite-sample approximations and demonstrate their accuracy via numerical examples.
Here, we investigate several tests based on small-sample approximations, and compare their performance in terms of α levels and power for different simulated situations, with continuous and discrete observations.
To estimate the covariances, we apply the large sample approximation according to Olkin and Siotani (1976).
Because of their small sample sizes, statistical methods based on large sample approximation are not appropriate for design and analysis of phase II trials.
