---
tag: 710VV73909
kind: concept
name: Kernel regression
msc: [62G08]
sources:
  - url: https://en.wikipedia.org/wiki/Kernel_regression
same_as:
  wikidata: Q1739319
  wikipedia: Kernel regression
---

## Summary

Kernel regression estimates the regression function $m(x) = E[Y \mid X = x]$ without assuming a parametric form for it.
The estimate at $x$ is a weighted average of the observed responses, with weights given by a kernel that favours observations with $X_i$ near $x$.
Its standard form is the Nadaraya–Watson estimator, a regression analogue of [[kernel density estimation|ZV65XMJ9A4]].

## Explanations

### L1 human

To guess the typical value of $Y$ at a point $x$, look at the data points whose $X$ is close to $x$ and average their $Y$ values.
Closer points get more weight, and the bandwidth decides how far "close" reaches.
For example, to estimate the typical weight of people of height $170$ cm, one averages the weights of people of nearby heights.
The result is a smooth curve through the cloud of data points.