Mathematical concepts I

Domination "The optimistic approach to MCO"
Try to find the best in all aspects product P.

Def: Domination in product space
P₁ dominates P₂ ( P₁ >> P₂), if $Y_{i1} \geq Y_{i2}, \, i = 1, 2, \ldots, Z$ and Y_j1 > Y_j2 for one $1 \leq j \leq Z$ .

Def: Domination in factor space
Given $\bf {X}_{1}$ and $\bf {X}_2$ which result in products $P_i := E(P(X_{i})), \; i=1,2$ .
$\bf {X}_{1}$ dominates $\bf {X}_2$ ( ${\bf X}_1 >> {\bf X}_2$ ), if P₁ >> P₂.

Idea: ${\bf X}_{opt}$ dominates complete factor-space.

This is formally nice and mathematically clean, but:

There may not exist a dominating object!

Dipl.-Stat. Detlef Steuer
1999-10-04