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Erschienen in:
2013 | OriginalPaper | Buchkapitel
Kernel Estimation of Regression Functions in the Boundary Regions
verfasst von : Tomasz Gałkowski
Erschienen in: Artificial Intelligence and Soft Computing
Verlag: Springer Berlin Heidelberg
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The article refers to the problem of regression functions estimation in the points near the edges of their domain. We investigate the model
$y_i = R\left( {x_i } \right) + \epsilon _i ,\,i = 1,2, \ldots n$
, where
x
i
is assumed to be the set of deterministic inputs,
x
i
∈
D
,
y
i
is the set of probabilistic outputs, and
ε
i
is a measurement noise with zero mean and bounded variance.
$R\left( . \right)$
is a completely unknown function. The possible clue of finding unknown function is to apply the algorithms based on Parzen kernel [5], [12]. The commonly known inconvenience of these algorithms is that the error of estimation dramatically increases if the point of estimation
x
is coming up to the left or right bound of interval
D
.
The main result of this paper is a new, original algorithm (named NMS) based on integral version of Parzen methods for estimation of edge values of a function
R
. The cross-validation-like technique is used in this procedure. The results of numerical experiments are presented.