14.3. (Sec. 14.3) The EM algorithm.

(3) If f and U are normal and f and X are observed. show that the likelihood function based on (xp.fl), ... ,(x.Ii,!,v) is

lb) Show that when the factor scores are included as data the sufficient set of statistics is i, j, Cu = C,lc) Show that the conditional expectations of the covariances in

(b) given X=(xl, ... ,XN), A, «1>, and 'if are C:, =.f( C"IX, A, «1>, 'if) = Cu '
C:[ = cC( C,[IX, A, «1>, 'if) = CxxC'if + A«I>A') -I A «I> , CfJ = cC( CrrlX, A, «1>, 'if) = «I> A '('if + A «I> A ') -IC,,('if + A«I>A') -I A«I>
+ «I> - «I> A '('if + A«I>A') -I A«I>.
ld) Show that the maximum likelihood estimators of A and 'if given «I> = I are

N 1 (2) TIP - x (x-4) 1 (2)11