In most cases when multiple predictors in a regression model are correlated with one another, there exists shared variance of the dependent variable among those correlated predictors.
If the expected value e exists, then the variance of ξ satisfies V[xi] leq int_{0}^{+infty} bigl 1-Phi(e+sqrt {x})+Phi (e-sqrt {x}) bigl 1-Phirm{d}x.
The details for deriving the unbiasedness of (2) are given in Appendix 2. However, when J or K are large, the inverse of X ′ X or A A ′ may not exist or the variance of the estimator may become unstable, and so we consider the ridge-type estimator given by begin{array}{*{20}l} hat{B}_{lambda,mu} =(X'X+lambda I_{J})^{-1}X'+mu(AA'+mu I_{K})^{-1}, end{array} (3).
However, such modest changes should not affect the predictive relationship between the bone turnover markers and BMD, should it exist, as the variance of rates of change was substantial in both markers and BMD.
Strain variance exists in most of the BoNT subtypes, and BoNT/B2 is not an exception.
Genetic variance exists for uniformity of BW in both environments but its low heritability implies that a large number of relatives are needed to reach even moderate accuracy of selection.
It is well known that there exists an analysis of variance (ANOVA) F-test for the problem of testing the equality of means from several independent samples under the assumptions of normality.
A large interpractice variance exists in the number of requested tests per 10 000 registered patients, the percentage of HIV tests per HIV-related consultation as well as the GP's initiative in discussing and testing for HIV that cannot be attributed to population density (table 1).
Still, we cannot rule out the existence of common environmental effects acting on the variance, and if they exist, the estimated genetic variance of the variance sub-model is probably inflated.
Lemma 3.1 For any sequence of independent random variables { ξ n, n ≥ 1 } with zero mean and finite variance, there exists a sequence of independent normal variables { Y n, n ≥ 1 } with E Y n = 0 and E Y n 2 = E ξ n 2 such that, for all q > 2 and y > 0, P ( max k ≤ n | ∑ i = 1 k ξ i − ∑ i = 1 k Y i | ≥ y ) ≤ ( A q ) q y − q ∑ i = 1 n E | ξ i | q, whenever E | ξ i | q < ∞, i = 1, …, n.
