Sufficient statistics

1. Jan 18, 2013

abeliando

1. The problem statement, all variables and given/known data
Problem is in the attachment, sorry, I can't figure out how to do tex in this message board system.

2. Relevant equations

3. The attempt at a solution
In the attachment.

Attached Files:

• t89M7Rg.png
File size:
86 KB
Views:
99
2. Jan 19, 2013

hikaru1221

I think you're into too much math. The I(.) function, if I get its meaning correctly, is nothing but to indicate that it is impossible to sample $x\leq\mu$. With frequentists' approach, this means a lot: you can safely ignore the bunch of I(.)'s and consider only those samples greater than $\mu$. This should solve the problem

3. Jan 19, 2013

Ray Vickson

Ignoring the fancy notation, what you have for given, fixed μ is that Y = X-μ is exponentially distributed with unknown mean, and you are trying to estimate that mean. You are being asked to show some property of the "usual" estimate.