How to pronounce“estimators”in English

regular asymptotically linear estimators of that functional.

And so robust estimators are designed to tolerate trade offs estimation error amongst the first step components

And so the estimators are going to look pretty similar.

all the estimators I'm going to show you are essentially estimating a mean of structured data.

Difference of mean estimators are generally okay in randomized trials but if you're in an observational study setting where propensity scores might vary.

And both of these estimators have very similar properties.

why these kinds of estimators or these kinds of properties arise.

So all the estimators I'm going to consider are going to have this kind of form.

Because despite these estimators being quite close to linear regression, they have many of the general structure that machine learning estimator typically has.

The linear regression estimators that I showed are only some examples and I now want to show some other algorithms that fall under the same kind of structure.

I think that the estimators of Pdoom are biased because of our biology, right?

And use this to debias estimators that use predictions from deep neural networks.

And so we derive robust and efficient estimators for descriptive moments, linear regression treatment effects identified through linear IV models, modern

And we also see that the estimators are also far away from one.

It's a kind of carefully designed estimators that start with a regression adjustment then use AIPW to correct the regression adjustment.

also apply to many other estimators.

To motivate the next kind of estimators that I want to look at, I want to consider one important example of using prediction methods in

So what we want is the granddaddy of all unsupervised density estimators, which is this thing that looks like this.

Another habit of good risk-takers is that they're good estimators and good at working with incomplete information.

And so I just wanted to debias some of my estimators, and I couldn't do that because they weren't, you know, the scenarios that come up a

also more powerful results about our learner type estimators.

And we're worried about how difference in means estimators deal with confounding.

We're training kind of arbitrary treatment effect estimators that kind of have the same type of confounding-robust behavior.

And then what these shared property of these estimators is that they kind of start with machine learning based estimates of the nuisance components.

Then the discrepancy between the feasible and oracle estimators, well, you can route it to order 4th root n.

Now, these were two estimators that we often call machine learning estimators, but honestly they are quite close to linear regression.

They also coming out of statistics the ridge estimators a very classical statistical estimator.

And so that's essentially like some of the most commonly used estimators.

Which then would allow you to extend this framework to kind of much more complicated estimators.

And you know, if we have two estimators, this is called double robustness, which is where the term double bias machine learning in

I'm going to start with descriptive means and then go on to other estimators.

At the end of the day, all these estimators are very similar because these are essentially all mean functionals, you know,

And the issue is kind of when you have these kinds of very biased estimators, it's essentially they're not going to have good rates of convergence.

And second, I said that among all unbiased estimators, it has low variance.

A regression tree tries to fit a different functional form than the linear regression type estimators that we discussed so far.

They begin allocating more money to their co-dot over or under estimators.

your structured data, any of those biases will propagate to estimators that rely on those predictions.

And so the second contribution is to identify estimators that are both unbiased and efficient.

So the existing literature kind of overwhelmingly doesn't worry about efficiency like we like efficient estimators, because I feel like economists

All right, so now I want to move on to the different estimators.

And so again, I'm going to illustrate this on commonly used estimators.

So far, we've discussed a number of treatment effect estimators and this leads to a natural question.

So, we're going to need to come up with some new ideas for evaluating estimators for CATE.

Anyways, so this is the first thing you can do to compare different treatment effect estimators it's to use the R-loss.

The conditions are again that this the these m hat, and he had estimators.

And just kind of the bigger picture is that now we've seen two different confounding robust estimators.

So that's all I'm going to say here other than kind of recommending the use of both estimators.

The first thing I want to do a deep dive on today is on failure modes for estimators of heterogeneous treatment effects.

And so we can use that theory to come up with well performing an efficient in terms of minimum variance estimators when we bring in machine learning.