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Convergence rate

As explained in Causal Inference for Data Science

A convergence rate describes how quickly an estimator or sequence approaches its limiting or expected value as sample size increases.

A convergence rate describes how quickly an estimator or sequence approaches its limiting or expected value as sample size n increases. For sequences of the form 1/n^a, larger positive a means faster convergence. section 8.1.2

Comparing 1/n and 1/√n

Both 1/n and 1/√n approach zero, but 1/n does so faster. A root-n consistent estimator approaches its expected value at rate 1/√n. The sample mean has this rate under the central limit theorem, and Double Machine Learning is proved to have it under stated assumptions. section 8.1.2

How Causal Inference for Data Science covers it

How deep it goes
Defines sequence rates and root-n consistency, then defers the DML proof to advanced mathematics.
Examples
Compares the sequences 1/n and 1/√n and uses the sample mean as a root-n benchmark.
What it assumes
Introduces sequence-rate intuition before formalizing estimator convergence and root-n consistency.
What you can do after
Evaluate estimator speed by comparing its convergence rate with the root-n benchmark.
How it connects
Connects estimators with sample means, the central limit theorem, Double Machine Learning, and causal effects.
Cover of Causal Inference for Data Science
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