Hello dear community,
I apologize for my english, but would like to ask how to show something like this?
the fisher-information is defined
the convexity is shown
a hyperplane is created
here we assume to have a density that minimizes the fisher information and we get a critical point.
and in the connection a theorem is set up where a Dirac delta is newly introduced.
and at the end a theorem and with it the main theorem
Theorem.....If the optimal g is everywhere strictly positive, then Djδxj (x) = 0. This is the Euler-Lagrange equation. It is non- linear and first order in g′(x)/g(x) for the best g. Without loss of generality, assume that g(0) = 1, as any scalar multiple of g will still be a solution. We now make the Riccati transformation.....
I don't understand why you have to show steps 1-4 and what the main theorem means!
I know it is a bit much, but I would appreciate any help.
Love greetings