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If X is a random variable from the uniform distribution on the interval [0,θ], how would one construct a 95% confidence interval for the method of moments estimator of θ?

I have found that enter image description here

and also its asymptotic distribution enter image description here

but I do not understand how to find a confidence interval for it. I know that I have to use the central limit theorem but I do not know how to apply it in this case.

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  • $\begingroup$ Yes, I saw this post. But I do not understand how chi-square is connected to the interval. can you suggest anything that would be helpful in understanding mentioned part? $\endgroup$
    – Mari Mtchedlishvili
    Commented Jan 13, 2023 at 19:07
  • $\begingroup$ If this is so, specify that part that you couldn't understand (or in fact you could leave a comment there once you have sufficient reputation). $\endgroup$
    – User1865345
    Commented Jan 13, 2023 at 21:32

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