The second study complemented the development of a Brief Core Set by comparing the categories of the Comprehensive Core Set that explained most of the variance of functioning and health [ 8].
The standard error for the parameters was estimated using a standard procedure to estimate the variance of a function about a point [ 41].
We can generalize the expectation and variance of a function of two or more random variables using Taylor series expansion.
In the eighties, new formulas for the variance of transfer function estimates based on high-order model approximations led to the first goal-oriented experiment design results.
The variance of a function (f in L^{2} (varOmega )) is simply operatorname{Var} [ f ] := mathbb{E} bigl[ f^{2} bigr] - mathbb{E} [ f ]^{2}.
As mentioned before, many decision-making problems usually contain a pile of fuzzy variables (xi_{1}, xi_{2}, ldots, xi_{n}), and it is thus required to calculate the variance of a function like (f xi_{1}, xi_{2}, ldots, xi_{n})).
Using the delta method, the variance of a function of two random variables X 1 and X 2 are defined as Var [ f ( X 1, X 2 ) ] ≈ ∂f ∂ X 1 ∂f ∂ X 2 Cov ( X 1, X 2 ).
Additionally, predictors that showed a similar variance of their function values, also showed a similar optimal λ.
Reduced spinal mobility and chest expansion and male gender made the largest contributions to explaining the variance of pulmonary function in the patient group.
ULM overcomes the problem of too strong smoothing of predictors with large QTL by building groups of m predictors showing similar variance of their function values and determining different λ for each group.
