<s>
In	O
statistics	O
,	O
kernel	B-Language
regression	I-Language
is	O
a	O
non-parametric	B-General_Concept
technique	O
to	O
estimate	O
the	O
conditional	O
expectation	O
of	O
a	O
random	O
variable	O
.	O
</s>
<s>
In	O
any	O
nonparametric	B-General_Concept
regression	O
,	O
the	O
conditional	O
expectation	O
of	O
a	O
variable	O
relative	O
to	O
a	O
variable	O
may	O
be	O
written	O
:	O
</s>
<s>
The	O
Nadaraya	B-Language
–	I-Language
Watson	I-Language
estimator	I-Language
is	O
:	O
</s>
<s>
Using	O
the	O
kernel	B-General_Concept
density	I-General_Concept
estimation	I-General_Concept
for	O
the	O
joint	O
distribution	O
f(x,y )	O
and	O
f(x )	O
with	O
a	O
kernel	O
K	O
,	O
</s>
<s>
which	O
is	O
the	O
Nadaraya	B-Language
–	I-Language
Watson	I-Language
estimator	I-Language
.	O
</s>
<s>
The	O
following	O
commands	O
of	O
the	O
R	B-Language
programming	I-Language
language	I-Language
use	O
the	O
npreg( )	O
function	O
to	O
deliver	O
optimal	O
smoothing	O
and	O
to	O
create	O
the	O
figure	O
given	O
above	O
.	O
</s>
<s>
According	O
to	O
David	O
Salsburg	O
,	O
the	O
algorithms	O
used	O
in	O
kernel	B-Language
regression	I-Language
were	O
independently	O
developed	O
and	O
used	O
in	O
fuzzy	B-General_Concept
systems	I-General_Concept
:	O
"	O
Coming	O
up	O
with	O
almost	O
exactly	O
the	O
same	O
computer	O
algorithm	O
,	O
fuzzy	B-General_Concept
systems	I-General_Concept
and	O
kernel	O
density-based	O
regressions	O
appear	O
to	O
have	O
been	O
developed	O
completely	O
independently	O
of	O
one	O
another.	O
"	O
</s>
<s>
MATLAB	B-Language
:	O
A	O
free	O
MATLAB	B-Language
toolbox	O
with	O
implementation	O
of	O
kernel	B-Language
regression	I-Language
,	O
kernel	B-General_Concept
density	I-General_Concept
estimation	I-General_Concept
,	O
kernel	O
estimation	O
of	O
hazard	O
function	O
and	O
many	O
others	O
is	O
available	O
on	O
(	O
this	O
toolbox	O
is	O
a	O
part	O
of	O
the	O
book	O
)	O
.	O
</s>
<s>
R	B-Language
:	O
the	O
function	O
npreg	O
of	O
the	O
np	O
package	O
can	O
perform	O
kernel	B-Language
regression	I-Language
.	O
</s>
<s>
Stata	B-Algorithm
:	O
,	O
</s>
