[R] Help: Maximum likelihood estimation

[dave fournier]

Actually it is not that difficult to parameterize the covariance matrix 
so that the
optimization is unconstrained. first parameterize the correlation matrix 
and the
standard deviations separately. the std devs can be parameterized as

       sigma_i=exp(x_i)     1<=i<=n

For the correlation matrix parameterize it in terms of its choleski 
decomposition.

this is a lower triangular matrix

    1      0       0
    a_1  a_2    0
    b _1 b_2 b_3
      ....


such that  the norm  of each row is 1

to ensure this  form start with

        1
       y_1  1
       y_2  y_3  1
         ...

  and normalize each row to have norm 1. There are n*(n-1)/2  of these y's.
  together with the n x_i's you have n*(n+1)/2 parameters as you should.