n**h
发帖数: 22 | 1 The Cramer-Wold theorem states that if every fixed linear combination of d
random variables converges to a normal distribution, then the d variables
jointly converges to a multivariate normal distribution. Does this theorem
hold when the dimension d goes to infinity? Thanks. |
h***i
发帖数: 3844 | 2 what is the meaning of infinitely dimensional multivariate normal
distribution?
【在 n**h 的大作中提到】
: The Cramer-Wold theorem states that if every fixed linear combination of d
: random variables converges to a normal distribution, then the d variables
: jointly converges to a multivariate normal distribution. Does this theorem
: hold when the dimension d goes to infinity? Thanks.
|
n**h
发帖数: 22 | 3 嗯，后来想了想，实际证明中一般都只用linear combination，不需要joint
distribution。
多谢! |
a***g
发帖数: 2761 | 4 maybe when the number of dimension goes to infinity, the joint normal
distribution can converge to the uniform distribution on the unit sphere in
an infinity dimensional space. |
