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kernel regression ：ウィキペディア英語版

kernel regression
: ''Not to be confused with Kernel principal component analysis.''
Kernel regression is a non-parametric technique in statistics to estimate the conditional expectation of a random variable. The objective is to find a non-linear relation between a pair of random variables ''X'' and ''Y''.
In any nonparametric regression, the conditional expectation of a variable

Y

relative to a variable

X

may be written:

\operatorname(Y | X) = m(X)

where

m

is an unknown function.
== Nadaraya-Watson kernel regression ==
and proposed to estimate

m

as a locally weighted average, using a kernel as a weighting function. The Nadaraya-Watson estimator is:

\widehat_h(x)=\frac

where

K

is a kernel with a bandwidth

h

. The fraction is a weighting term with sum 1.

抄文引用元・出典: フリー百科事典『ウィキペディア（Wikipedia）』
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