Cramér-Wold theorem
Let
ˉXn=(Xn1,…,Xnk)andˉX=(X1,…,Xk) |
be random vectors. Then ˉXn converges to ˉX in distribution (http://planetmath.org/ConvergenceInDistribution) if and only if
k∑i=1tiXni𝐷→n→∞k∑i=1tiXi. |
for each (t1,…,tk)∈ℝk. That is, if every
linear combination of the coordinates
of ˉXn converges in distribution to the correspondent linear combination of coordinates of ˉX.
Title | Cramér-Wold theorem |
---|---|
Canonical name | CramerWoldTheorem |
Date of creation | 2013-03-22 13:14:21 |
Last modified on | 2013-03-22 13:14:21 |
Owner | Koro (127) |
Last modified by | Koro (127) |
Numerical id | 4 |
Author | Koro (127) |
Entry type | Theorem |
Classification | msc 60E05 |