<s>
In	O
statistics	O
,	O
semiparametric	B-General_Concept
regression	I-General_Concept
includes	O
regression	O
models	O
that	O
combine	O
parametric	B-General_Concept
and	O
nonparametric	B-Language
models	O
.	O
</s>
<s>
They	O
are	O
often	O
used	O
in	O
situations	O
where	O
the	O
fully	O
nonparametric	B-Language
model	O
may	O
not	O
perform	O
well	O
or	O
when	O
the	O
researcher	O
wants	O
to	O
use	O
a	O
parametric	B-General_Concept
model	I-General_Concept
but	O
the	O
functional	O
form	O
with	O
respect	O
to	O
a	O
subset	O
of	O
the	O
regressors	O
or	O
the	O
density	O
of	O
the	O
errors	O
is	O
not	O
known	O
.	O
</s>
<s>
Semiparametric	B-General_Concept
regression	I-General_Concept
models	O
are	O
a	O
particular	O
type	O
of	O
semiparametric	O
modelling	O
and	O
,	O
since	O
semiparametric	O
models	O
contain	O
a	O
parametric	B-General_Concept
component	O
,	O
they	O
rely	O
on	O
parametric	B-General_Concept
assumptions	O
and	O
may	O
be	O
misspecified	O
and	O
inconsistent	O
,	O
just	O
like	O
a	O
fully	O
parametric	B-General_Concept
model	I-General_Concept
.	O
</s>
<s>
Many	O
different	O
semiparametric	B-General_Concept
regression	I-General_Concept
methods	O
have	O
been	O
proposed	O
and	O
developed	O
.	O
</s>
<s>
The	O
parametric	B-General_Concept
part	O
of	O
the	O
partially	O
linear	O
model	O
is	O
given	O
by	O
the	O
parameter	O
vector	O
while	O
the	O
nonparametric	B-Language
part	O
is	O
the	O
unknown	O
function	O
.	O
</s>
<s>
with	O
and	O
the	O
model	O
allows	O
for	O
a	O
conditionally	O
heteroskedastic	B-General_Concept
error	O
process	O
of	O
unknown	O
form	O
.	O
</s>
<s>
This	O
method	O
is	O
implemented	O
by	O
obtaining	O
a	O
consistent	O
estimator	O
of	O
and	O
then	O
deriving	O
an	O
estimator	O
of	O
from	O
the	O
nonparametric	B-Language
regression	I-Language
of	O
on	O
using	O
an	O
appropriate	O
nonparametric	B-Language
regression	I-Language
method	O
.	O
</s>
<s>
The	O
single	O
index	O
model	O
takes	O
its	O
name	O
from	O
the	O
parametric	B-General_Concept
part	O
of	O
the	O
model	O
which	O
is	O
a	O
scalar	O
single	O
index	O
.	O
</s>
<s>
The	O
nonparametric	B-Language
part	O
is	O
the	O
unknown	O
function	O
.	O
</s>
<s>
using	O
kernel	B-General_Concept
method	O
.	O
</s>
<s>
the	O
leave-one-out	B-General_Concept
nonparametric	B-General_Concept
kernel	I-General_Concept
estimator	O
of	O
.	O
</s>
<s>
where	O
is	O
the	O
leave-one-out	B-General_Concept
estimator	O
.	O
</s>
