That R at the start effectively allows only rows where Y is measured to have non-zero contributions to the estimating equations. This covers Step 1 - ThreadSky

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pausalz.bsky.social • 16 days ago

That R at the start effectively allows only rows where Y is measured to have non-zero contributions to the estimating equations.

This covers Step 1

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pausalz.bsky.social•16 days ago

Step 2-3 can be done in the same estimating equation. We simply want the predicted values of Y and then the estimating equation for the mean. The following shows this notationally

pausalz.bsky.social•16 days ago

Now that we have each of the pieces, we can simply stack the estimating functions into a column vector. This gives us our entire estimator, where all the pieces are estimated simultaneously

pausalz.bsky.social•16 days ago

Given that these are equivalent ways of programming the same estimator, why bother with the M-estimator?

The reason is that the M-estimator also gives us a way to estimate the variance directly. We can simply use the sandwich variance

pausalz.bsky.social•16 days ago

Why? Well it is because the sandwich variance 'automates' the delta method (we will return to why this is in a future week). This means we can estimate the variance of \mu while incorporating the uncertainty in estimating \beta. We don't have to bother with the bootstrap!!

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