I`m trying to find an answer, but i have some problems, help.Let P θ =...

Kassandra Ross

Kassandra Ross

Answered

2022-06-24

I`m trying to find an answer, but i have some problems, help.
Let P θ = U [ 0 , θ ].
For h , θ 0 > 0 and Z e x p ( 1 θ 0 ) I have to show that:
d P θ 0 h / n n d P θ 0 n d , P θ 0 n e h θ 0 1 { Z h }
I already proved that for Z n = n ( θ 0 max { X 1 , , X n } ) with X 1 , X n P θ 0 holds Z n D Z and this task seems like I have to prove that the pdf is converging too. I'm not sure which technical steps I need to show this and I'm not sure which kind of convergence is meant by d , P θ 0 n .

Answer & Explanation

Govorei9b

Govorei9b

Expert

2022-06-25Added 21 answers

The convergence follows with Radon-Nikodym, Slutzky and continuous mapping theorem.
d P θ 0 h / n n d P θ 0 n = d P θ 0 h / n n d λ ( d P θ 0 n d λ ) 1 = ( θ 0 θ 0 h n ) n 1 { 0 X i θ 0 h / n   i } 1 { 0 X i θ 0   i } = ( θ 0 θ 0 h n ) n 1 { Z n h } Slutzky e x p ( h θ 0 ) 1 { Z h }

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get your answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?