Hi, so I understand that the delta method means finding the distribution of some function of B, F(b) through taylor expansion.
And through this process, we get that:
$$ F(b) = N( f(b), \Gamma * \Sigma_\beta * \Gamma') $$
Where gamma = df/db
So in this case I would think:
$$ B ~ ( \delta_0 / \gamma_0 , \Gamma* \Sigma_\beta * \Gamma' ) $$
$$ Where: \Gamma = [df/d\delta, df/d\gamma ] $$ $$ So: \Gamma = [1/\gamma , \frac{- \delta}{\gamma^{2}}] $$
But I am not sure what is: $$ \Sigma_\beta $$
I am also unsure how to solve the second part of the problem. I know I have to use the test statistic (where little r is what we think the coefficients should equal:
$$ ( F(b) - [ r ] )' ( \Gamma \Sigma_\beta \Gamma' )^{-1} (F(b) -r ) $$
If the H_0 : $$ F(b) = \delta_0 / \gamma_0 = 1 $$
Then does $$ \Gamma $$ remain the same as above and r = 1?
