Method Derived from Likelihood

• The Likelihood

  

• so, the principle of maximizing the likelihood is equivalent to minimizing where

  

  with respect to N theoretical parameters in .

• (i) Notice that is the sum where are independent Gaussian random variables of unit standard deviation and zero mean.

• We calculate distribution exactly, but in practice this is rarely necessary. Thus, we can easily show that---for fixed ---that

  

• and this is sufficient for large N as central limit theorem says will be Gaussian with above mean and standard deviation.