# Kernel regression

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The Kernel regression is a non-parametrical technique in statistics to estimate the conditional expectation of random variable.

In any nonparametric regression, the conditional expectation of a variable $Y$ relative to a variable $X$ may be written:

$\operatorname{E}(Y | X)=m(X)$

where $m$ is a non-parametric function.

Nadarya (1964) and Watson (1964) proposed to estimate $m$ as a locally weighted average, using a kernel as a weighting function. The Nadarya-Watson estimator is:

$\widehat{m}_h=\frac{n^{-1}\sum_{i=1}^nK_h(x-X_i)Y_i }{n^{-1}\sum_{i=1}^nK_h(x-X_i)}$

where $K$ is a kernel with a bandwith $h$.

## Statistical implementationEdit

 kernreg2 y x, bwidth(.5) kercode(3) npoint(500) gen(kernelprediction gridofpoints)