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Exact(12)
Then, substitute (12) into (9), ρ(C,U) is obtained, with which the standard variances, a(d), b(d), and C d) in (8) can be worked out.
Two approaches are considered for the reference variances: a classical F-test and interval hypothesis testing.
Then, the shadow fading can be decomposed as ε C = W + W C ε U = W + W U (7). where W, WC, and WU are independent Gaussian random variables with zero mean and standard variances a, b, and c, respectively, and they satisfy σ C 2 = a 2 + b 2 σ U 2 = a 2 + c 2 E ε C ε U = a 2 = ρ C,U σ C σ U (8).
As expected, we find that the asymptotic estimated covariance a 12 is close to zero for r = 0 and it is close to the variance for r = 1. Figure 4(c) demonstrates that the interplay between covariances a 12 and variances a 11 and a 22 leads to a sublinear dependence of the asymptotic correlation coefficient ρ T = a 12 / ( a 11 a 22 ) (Eq. (33)) in the large time bin limit, T = 25 τ s.
For those data sets for which the transformation did not allow to obtain homogeneous variances, a more conservative level of significance was considered [38].
In the case of unequal variances, a non-parametric test was performed by applying the above-described permutational ANOVA to the ranks of the original data.
Similar(47)
The heritability h2 relates the additive variance within a population to the total variance: V A, w = h2 V w.
Through weighting both means with their inverse variance, a combined estimator is derived.
Due to unequal variance, a Kruskal-Wallis nonparametric test was used for comparison of groups.
To reduce the estimation variance, a least-squares HOYW (LSYW) method can be used [2].
While different designs may reduce the variance, a perfectly flat coupler theoretically cannot be built.
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