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Additional info for A statistical method for the estimation of window-period risk of transfusion-transmitted HIV in dono

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We refer to constraints of the form ai. x :S lai (i = 1, 2, ... , m) as lower constraints, and to those of the form aix:s b i + lai (i = 1, 2, ... , m) as upper constraints. We shall assume that the intersection of the lower constraints with the positive hyper octant is nonempty. This means that for any realization of the vector b (q) (except a set of measure e) there exi sts at least one feasible plan. bi - Using the foregoing concepts, we formulate without proof a sufficient condition for the stochastic e-stability of a solution in the mean.

8) implies constancy of the set of labeled indices with probability 1- e. 8). 9) where T = {y: yTA ~ CtY ~ o}. 9). This ensues from the following lemma. 1. 9) have a unique optimal plan. Also, let the solution in the mean x* of the primal problem be e-stable. Then the solution in the mean y* of the dual problem is also e-stable. Proof. 1). 9) have a unique optimal plan. For any q E Wq the optimal extreme point is the point of intersection of labeled hyperplanes numbered it, ... , i k , h, ... , jz.

We define a e (z, a) = 'f (x) = x, z = y, + ~ (y); t (z, a) = g (x) + h (y) - b, ex (a) = T (b, x). 1 to prove the convexity of a(a) and convexity of y(b, x) on x. 2. 2 are met. Proof. If y (b, x) is convex on x for all fixed vectors b, integration over the distribution of b always yields a function Ey (b, x) convex on x. 1). , it is 52 V. V. KOLBIN required to solve the problem E min"[ (b, x) x = E min min {? (x) x y + 'Ji (y) I g (x) + h (y) :;;.. b}. 8) The following theorem holds. 3. Let x(Eb) be a solution of the problem minl(Eb,x).

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