<s>
A	O
kernel	B-General_Concept
smoother	I-General_Concept
is	O
a	O
statistical	O
technique	O
to	O
estimate	O
a	O
real	O
valued	O
function	O
as	O
the	O
weighted	O
average	O
of	O
neighboring	O
observed	O
data	O
.	O
</s>
<s>
Kernel	B-General_Concept
smoothing	I-General_Concept
is	O
a	O
type	O
of	O
weighted	O
moving	O
average	O
.	O
</s>
<s>
In	O
the	O
following	O
sections	O
,	O
we	O
describe	O
some	O
particular	O
cases	O
of	O
kernel	B-General_Concept
smoothers	I-General_Concept
.	O
</s>
<s>
The	O
Gaussian	B-Algorithm
kernel	I-Algorithm
is	O
one	O
of	O
the	O
most	O
widely	O
used	O
kernels	O
,	O
and	O
is	O
expressed	O
with	O
the	O
equation	O
below	O
.	O
</s>
<s>
The	O
idea	O
of	O
the	O
nearest	B-General_Concept
neighbor	I-General_Concept
smoother	O
is	O
the	O
following	O
.	O
</s>
<s>
For	O
each	O
point	O
X0	O
,	O
take	O
m	O
nearest	B-General_Concept
neighbors	I-General_Concept
and	O
estimate	O
the	O
value	O
of	O
Y(X0 )	O
by	O
averaging	O
the	O
values	O
of	O
these	O
neighbors	O
.	O
</s>
