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The CR Lower Bound

Lyrics copyright by Kyle White and Bradley Turnbull
May be sung to the tune of "Jerk It Out" (Caesars)

Theta one, theta two, which estimator do I choose?
Both of them unbiased, what now? I'm still so confused.
I need a better measure than just looking at means. Calculating variance is smart, it seems.
So here we go!

'Cause it's easy when you know how it's done.
Invert the information when the bias is none.
Can't beat it, bounded from below!
C-R lower bound!

Too bad my stat is lacking some efficiency.
Why can't someone out there tell how to fix this please?
Sufficient estimators will do the trick --
condition on them, that will be my fix!
So thank you Rao!

'Cause it's easy when you know how it's done.
Improve an estimator with a sufficient one.
Just try it, you've got nothing to lose!
Rao-Blackwell improves!

'Cause it's easy when you know how it's done.
Invert the information when the bias is none.
Can't beat it, bounded from below!
C-R lower bound

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