Marc Raimondo - CMI

Theme
� Many problems of classical multivariate statistics involve
eigenvalues x1 > x2 > ... > xp
� Asymptotics in p ⇒ useful information, [even p small]
� Illustrate for null distributions for x1
Example: (multiple) Regression.
y = X β + ǫ
n×p n×q q×p n×p
ǫ ∼ N(0,In ⊗ Ip).
Tests of H0 : β = 0 use roots of det[A + xi(A + B)] = 0.
A = SSH = ˆ β T X T X ˆ β “Hypothesis”
B = SSE = y T (I − PX)y “Error”
Luminy 12/08 – p.9