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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 $H_n$ :

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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

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  • $\begingroup$ 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. $\endgroup$ – Glen_b -Reinstate Monica Nov 25 '19 at 10:33

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