Estimation

• Use a t

may sing to tune of "Let it Be" (Paul McCartney/Beatles)

When I find myself with normal data,
William Gosset comes to me
Speaking words of wisdom, Use a t.

If my NP plot is linear
but sigma isn't known to me
This is not a problem, Use a t.

Use a t, use a t, use a t, use a t
Student knows the answer: Use a t.

And when the broken hearted students
in a stats class can't agree
You can show the answer: Use a t.

Some want to use a Z test,
and a chi-square is a mystery
The truth is very simple: Use a t

Use a t, use a t, use a t, use a t
Student knows the answer: Use a t.

And when your thoughts are cloudy,
RA Fisher may not hear your plea
But Gosset will deliver, with a t.

He knows you are trying
and he wants to set your mind at ease
Don't think twice about it, use a t.

Use a t, use a t, use a t, use a t
Student knows the answer: Use a t.

• MLE

may sing to tune of "Let it Be" (Paul McCartney/Beatles)

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.

• It Don't Mean A Thing (If You Don't Do Modelling!)

Sung by Gurdeep Stephens. Lyrics copyright and music performed by Michael Greenacre.
May sing to tune of "It Don't Mean a Thing (If It Ain't Got That Swing)" (Duke Ellington and Irving Mills)

It don't mean a thing if you don't do modelling,
Doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-waah
It don't mean a thing if you don't do modelling,
Doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-waah

It don't matter if you're frequentist or Bayesian,
You just need a model with some alphas and betas, and x's and y's, and i's and j's and k's in

So it don't mean a thing if you don't do modelling
Doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-waah
It don't mean a thing if you don't do modelling,
Doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-wah-doo-waah
Doo-wah-doo-wah-doo-wah-doo-wah - doo-wah-doo-wah - wah!

• The model I Love

Sung by Gurdeep Stephens. Lyrics copyright and music performed by Michael Greenacre.
May sing to tune of "The Man I Love" (George Gershwin)

Some day it'll come along
The model I love,
It'll be robust and strong
The model I love,
And when it comes my way
I'll put it on my resume!

Of all the models out there,
Is there one for me?
I'll give it all my love and care,
Mathematically,
And then - finally,
I'll get my PhD

Maybe I'll do estimation
Using likelihood, or least-squares,
Or with some approximation,
Or just eyeballin',
That's the job we're all in.

To get some publications,
I'll write papers, at least two,
For my job applications,
I think that'll do, don't you?
So hear me, Lord above, I'm waiting for that model I love,
I'm waiting for the model I love.

• It Ain't Necessarily So

Sung by Gurdeep Stephens. Lyrics copyright and music performed by Michael Greenacre.
May sing to tune of "It Ain't Necessarily So" (George Gershwin)

It ain't necessarily so
It ain't necessarily so
That for models to be formal
Data have to be normal
But it ain't necessarily so

My data had values real skew,
Relationships nonlinear too,
But with spline-approximation
Or Box-Cox-transformation
My data are more normal than you.

Now it ain't necessarily so
That your deviance has to be low,
Use less parameters, (pronounce: paramee-ters)
Less alphas and betas,
Then apply Akaike,
Although it sounds freaky,
And less will be more as you know...

It ain't necessarily so
It ain't necessarily so
That for models to be formal
Data have to be normal
But it ain't necessarily so.
It ain't necessarily - It ain't necessarily
It ain't necessarily - It ain't necessarily
It ain't necessarily - It ain't necessarily
It ain't necessarily SO!

• Summertime

Sung by Gurdeep Stephens. Lyrics copyright and music performed by Michael Greenacre.
May sing to tune of "Summertime" (George Gershwin)

It's summertime,
Statistical modelling is easy,
Data are fitting,
Explained variance is high.

So hush, statisticians, don't you cry

• Call It Maybe

Lyrics ©2013 by Lawrence Mark Lesser
May be sung to the tune of "Call Me Maybe" (Carly Rae Jepsen, Tavish Crowe, and Josh Ramsay)

I went to find people's heights, I measured each person thrice:
The numbers didn't match nice - and I said "Oy vey!"
When I was asked for the mean, I knew I had to come clean:
I said it's something between - and I gave a range.

Climb: That's variation: There is correlation
with stat education, knowin' what's exact or maybe.

CHORUS: Hey, I don't know mu - and that's not crazy,
But here's my window: call it maybe.
I can't say I'm right; I'm not laaaaazy:
There's always error, so call it maybe.
Hey, life's uncertain, and that's not crazy,
But here's my window: call it maybe.
No way to know mu - quite exaaaaactly,
But here's my window: call it maybe.

I give my best argument - so I can feel confident
At ninety-five percent - for what I portray.
I need a sense of how far - from my sample's x-bar
My true parameters are: that's just the way.

(Repeat Climb, Repeat Chorus)

Bridge: Before I took a class in stats, I reasoned so bad,
Before I took a class in stats, I reasoned so bad,
And you should know that - I reasoned so, so bad!

(Repeat Chorus, omitting vocals over first quarter;
Repeat Bridge, except last 6 words)

So call it maybe!

• The CR Lower Bound

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

Watch the video