“MLE”

lyric © 2007 Lawrence M. Lesser (sing to tune of Lennon & McCartney’s “Let it Be”)

When I’m in need of estimation, Ronald Fisher comes to me,

Speaking words of wisdom: MLE.

And though there may be bias, this will vanish asymptotically,

Speaking words of wisdom: MLE

MLE, MLE, MLE, MLE, whisper words of wisdom, MLE.

And when the statisticians put a focus on efficiency,

There will be an answer: MLE.

For samples really large, tell me: where’s the lowest M.S.E.?

There will be an answer: MLE.

MLE, MLE, MLE, MLE, there will be an answer, MLE.

And when a theta hat is found to be theta’s MLE,

Then g of theta has what MLE?

Well, if g is 1-to-1, an invariance property

Says g of theta hat is the MLE.

MLE, MLE, MLE, MLE -- the most likely answer is MLE.

MLE, MLE, asymptotic normality -- whisper its precision, MLE.