---
tag: J7410PG2DR
kind: concept
name: Robust statistics
msc: [62F35, 62G35]
sources:
  - url: https://en.wikipedia.org/wiki/Robust_statistics
same_as:
  wikidata: Q1665389
  wikipedia: Robust statistics
---

## Summary

Robust statistics studies statistical procedures whose results change little when the data depart slightly from the model assumptions.
Such departures include outliers or a heavier tail than assumed.
Two main measures of robustness are the [[breakdown point|BRGGGZVQDS]] and the [[influence function|EB2QJQNE5Z]].
The first says how much bad data an estimator can absorb, and the second how much a single point can move it.
Typical robust procedures are the median, trimmed means and other [[L-estimators|E3C4F0RKJY]], and Huber's [[M-estimators|4503R8BVF8]].
The field was shaped by Tukey, Huber and Hampel from the 1960s on.

## Explanations

### L1 human

The average of a list of incomes can jump enormously when one billionaire joins the list.
The median barely moves.
Robust statistics prefers methods like the median, which give sensible answers even if a few data points are wrong or extreme.
It also studies the price of this safety, since robust methods are often a little less precise when the data really are clean.