“Comparing Apples and Oranges: Two Examples of the Limits of Statistical Inference, With an Application to Google Advertising Markets” is our analysis of Google AdSense Channel IDs and our use of the Cramer Rao bound to show that these IDs fundamentally limit what participants in the Google online advertising market can measure (and therefore in turn limit what these players can do).

We also include a entry level exposition and examples of what the Cramer Rao Inequality is and how it works.

This is a repost of an older paper- but a few people have pointed out they were put off by the incredibly uninformative title of the original post “New Paper.”

Categories: Administrativia Expository Writing Mathematics

### jmount

Data Scientist and trainer at Win Vector LLC. One of the authors of Practical Data Science with R.

This is exactly why you shouldn’t be using unbiased estimation. Bayesian estimation avoids all these problems and is consistent with what your actually trying to do: maximize profit.

@John

A very interesting point. I would caution that the likelihoods you would want to calculate (say in the section 3.2.1 example) in a Bayesian procedure would essentially be functions of the summary statistics that are not very tightly related to the parameters you are trying to estimate (due to the unfortunate censoring process of only being allowed a constant number nearly co-linear measurements). So I think you run into similar problems. As the number of (hidden) data items gets large I would expect the Bayesian estimate to get near the linear algebra estimate (which is itself having trouble). I emphasize that the unfortunate sum-ups were not part of the estimation procedure, but part of the externally imposed problem structure.