Homework 4.  Statistics 771, Spring 09
Posted online Wednesday March 11/09
Due in class Monday March 23/09.


1. Consider a generic missing data problem involving observable data 
   X and missing data Z, governed by a joint density p(x,z|theta) for
   an unknown parameter theta.  The problem is to show 
   how the observed information [from the actual loglikelihood
   l(theta) = log p(x|theta) ] is diminished compared to the expected
   value, taken conditionally upon X=x, of the would-be observed
   information [from the complete data loglikelihood l_c(theta)
   = log p(x,z|theta) ].  Recall that observed information is computed
   as the negative second derivative of the (corresponding) log likelihood.
   You may assume sufficient regularity that Fisher information (variance
   of score) equals the expectation of observed information, at a given
   parameter value.