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Erschienen in:
2014 | OriginalPaper | Buchkapitel
Nonparametric Function Fitting in the Presence of Nonstationary Noise
verfasst von : Tomasz Galkowski, Miroslaw Pawlak
Erschienen in: Artificial Intelligence and Soft Computing
Verlag: Springer International Publishing
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The article refers to the problem of regression functions estimation in the presence of nonstationary noise. We investigate the model
$y_i = R\left( {{\bf x _i}} \right) + \epsilon _i ,\,i = 1,2, \ldots n$
, where
x
i
is assumed to be the
d
-dimensional vector, set of deterministic inputs,
x
i
∈
S
d
,
y
i
is the scalar, set of probabilistic outputs, and
ε
i
is a measurement noise with zero mean and variance depending on
n
.
$R\left( . \right)$
is a completely unknown function. One of the possible solutions of finding function
$R\left( . \right)$
is to apply non-parametric methodology - algorithms based on the Parzen kernel or algorithms derived from orthogonal series. The novel result of this article is the analysis of convergence for some class of nonstationarity. We present the conditions when the algorithm of estimation is convergent even when the variance of noise is divergent with number of observations tending to infinity. The results of numerical experiments are presented.