The singular mixed linear model with constraints is investigated with respect to an influence of inaccurate variance components on a decrease of the confidence level. The algorithm for a determination of the boundary of the insensitivity region is given. It is a set of all shifts of variance components values which make the tolerated decrease of the confidence level only. The problem about geometrical characterization of the confidence domain is also presented.

When we apply stacked regression to classification we need only discriminant indices which can be negative. In many situations, we want these indices to be positive, e.g., if we want to use them to count posterior probabilities, when we want to use stacked regression to combining classification. In such situation, we have to use leastsquares regression under the constraint βₖ ≥ 0, k = 1,2,...,K. In their earlier work [5], LeBlanc and Tibshirani used an algorithm given in [4]. However, in this paper...

Biology and medicine are not the only fields that present problems unsolvable through a linear models approach. One way to overcome this obstacle is to use nonlinear methods, even though these are not as thoroughly explored. Another possibility is to linearize and transform the originally nonlinear task to make it accessible to linear methods. In this aricle I investigate an easy and quick criterion to verify suitability of linearization of nonlinear problems via Taylor series expansion so that...