# Asymptotic Distribution of Wald test

If $$X_1 , X_2 , ... X_n$$ are iid and they have the same pdf $$f_θ(x)$$ .

Consider testing $$H_0 : θ= θ_0$$ vs $$H_n : θ = θ_0 +Δ * n^{-1/2}$$.

where , $$Δ = (Δ_1 , Δ_2 , .. Δ_k)^T$$

We want to find the asymptotic distributions of the Wald and Rao Test Statistics under $$H_n$$ :



I think the file below has the answer but I am not completely sure if it is exactly the same.

FILE At the end of page 13, You can find Corollary 1 in the results, 17 and 18 are the same but what about the values of $$D$$ and $$t$$? Are those the same in both cases? How can I find $$D$$ and $$t$$

https://www.stat.washington.edu/jaw/COURSES/580s/581/LECTNOTES/ch4-rev1.pdf

• While "finding a file" does fall under "search and research", a necessary step in any good question, it is not in any sense your own work and so doesn't seem to meet the needs of what appears to be a self-study question. – Glen_b -Reinstate Monica Nov 25 '19 at 10:33