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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)

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