Comparing Apples and Oranges: Two Examples of the Limits of Statistical Inference, With an Application to Google Advertising Markets

TL;DR

This paper explores the fundamental limits of statistical inference in estimating multiple parameters simultaneously, using Google advertising data as a case study to illustrate the constraints imposed by the Cramer-Rao bound.

Contribution

It demonstrates how the Cramer-Rao bound constrains the accuracy of estimating numerous Google Ad campaign metrics and highlights the limitations in large-scale A/B testing.

Findings

The Cramer-Rao bound sets a fundamental limit on estimation accuracy.

Simultaneous estimation of many parameters faces inherent precision constraints.

Implications for large-scale online experiments and advertising analytics.

Abstract

We show how the classic Cramer-Rao bound limits how accurately one can simultaneously estimate values of a large number of Google Ad campaigns (or similarly limit the measurement rate of many confounding A/B tests).