The saddlepoint vector
is the solution to the equation
is the diagonal matrix
with diagonal element equal to ,
written compactly (borrowing efficient MATLAB notation) as
where are the elements of vector
where is a vector of 1's.
The saddlepoint approximation for
is given by
where operates separately on each element and
borrows the efficient MATLAB notation
for element-wise exponentiation by .
To find the saddlepoint, we initialize
to zeros, then implement the iterative
Newton-Raphson search for the saddlepoint
as described in . For convenience, a MATLAB
implementation is provided below in section 16.6.3.