Sentence examples for usual variance from inspiring English sources

We show (i) that the usual sampling variance estimator is a downward-biased estimator of the total variance of the abundance index, (ii) that the bias of the usual variance estimator does not decrease when increasing the sampling size, (iii) that correlated observation errors may have a dramatic impact on the total variance, especially when the sampling size increases.

There are the usual variance decompositions, begin{aligned} Sigma _{SS}=Sigma _{hat{S}hat{S}}+Sigma _{epsilon epsilon },quad Sigma _{NN}=Sigma _{hat{N}hat{N}}+Sigma _{epsilon epsilon }, end{aligned} (26 the first following from the decomposition (S=hat{S}+left( S-hat{S} right) ), whose components are uncorrelated by (22), and analogously for the second.

Let p be a real density function defined on a compact subset Ω of R m, and let E ( f, p ) = ∫ Ω p f d ω be the expectation of f with respect to the density function p. In this paper, we define a one-parameter extension Var γ ( f, p ) of the usual variance Var ( f, p ) = E ( f 2, p ) − E 2 ( f, p ) of a positive continuous function f defined on Ω.

SPV may also be estimated by 1/VIF, where VIF is the usual variance inflation factor [cf. [ 26]].

Additional simulations (data not shown) indicated that this problem could be solved by use of Wald tests incorporating robust 'information sandwich' variance estimates [ Huber, 1967], rather than likelihood ratio tests or Wald tests with the usual variance estimate (which equals minus the inverse of the Hessian matrix).

The usual bias-variance trade-offs neatly encapsulated in the traditional mean-square error loss need to make way for methods that reorient some of the focus toward assessing classification ability.

The first method is the usual inverse-variance method and the second method is an alternative approach proposed by Knapp and Hartung [ 19].

For comparisons among more than three groups, Kruskal-Wallis test was used in place of the usual analysis of variance (ANOVA), because Bartlett's test revealed that the group variances were significantly different in all such cases.

However, an underlying assumption for the validity of the usual analysis of variance for a complete factorial design is that the runs are observed in a completely randomized order [ 8].

where ΔT is the time interval between successive scans and v k is a zero-mean Gaussian noise vector with covariance cov[v k ] = Q = diag(q x, q y, qℓ), where q x and q y are the usual acceleration noise variances for the constant velocity model.

then in view of the usual meaning of the variance, we tend to think that this generalized hierarchical teaching model is better than the generalized traditional teaching model.