# Thread: Statistical estimation (classical) question

1. ## Statistical estimation (classical) question

Each worker's productivity Xi(where i=1,2,3,4....n) is distributed uniformly and independently on the interval (0,L), where L is an unknown upper limit, which we want to estimate
Notice: L(Tilda) is an estimator of L
a) The probability function density function in terms of L?
b) Find E(xi) in terms of L?
c) Find var(xi) in terms of L?
d) Estimated L using L(tilda)= 2X(bar), where X(bar) is based on X1, X2,...Xn
Find the bias of L(tilda)?
e) Find the MSE of L(tilda)? is L(tilda) a consistent estimator of L?
f) On inspecting the actual values X1, X2, Xn, we discards the estimator L(tilda), muttering curses on classical estimation theory, and estimates L another way. Can you see why we have might done so? The reason is good, by the way it's not a bayesian; and not all samples of X1, X2, Xn would cause him to react this way

Have worked through some of the sub-questions, but far from sure about the correctness of the answers!

Best regards

2. post what you have
this point estimator is just the method of moments estimator from a U(0,L) distribution.
A better estimator is the MLE, which is

${n+1\over n} X_{(n)}$

where that rv is the largest order stat.

Interstingly using my weird strong laws I'm runing simulations on a new estimator from this very distribution.
It's a resampling idea I thought of this past summer, that seems to work.