Question

Unbiased estimator of uniform distribution

Answer 1

Let xixi be iid observations in a sample from a uniform distribution over [0,θ][0,θ]. Now I need to estimate θθ based on NN observations and I want the estimator to be unbiased.

I thought about simple estimator θ^=max(xi)θ^=max(xi).

Based on simulation it is not biased, yet I couldn't show it analytically.

Could anyone, please, show it is unbiased?

BTW, I could easily find another, easy to prove, unbiased estimator, θ^=2mean(xi)

I hope help u