<s>
In	O
statistics	O
,	O
a	O
parametric	B-General_Concept
model	I-General_Concept
or	O
parametric	B-General_Concept
family	O
or	O
finite-dimensional	O
model	O
is	O
a	O
particular	O
class	O
of	O
statistical	O
models	O
.	O
</s>
<s>
Specifically	O
,	O
a	O
parametric	B-General_Concept
model	I-General_Concept
is	O
a	O
family	O
of	O
probability	O
distributions	O
that	O
has	O
a	O
finite	O
number	O
of	O
parameters	O
.	O
</s>
<s>
The	O
model	O
is	O
a	O
parametric	B-General_Concept
model	I-General_Concept
if	O
for	O
some	O
positive	O
integer	O
.	O
</s>
<s>
A	O
parametric	B-General_Concept
model	I-General_Concept
is	O
called	O
identifiable	O
if	O
the	O
mapping	O
is	O
invertible	O
,	O
i.e.	O
</s>
<s>
Parametric	B-General_Concept
models	I-General_Concept
are	O
contrasted	O
with	O
the	O
semi-parametric	O
,	O
semi-nonparametric	B-General_Concept
,	O
and	O
non-parametric	B-General_Concept
models	I-General_Concept
,	O
all	O
of	O
which	O
consist	O
of	O
an	O
infinite	O
set	O
of	O
"	O
parameters	O
"	O
for	O
description	O
.	O
</s>
<s>
in	O
a	O
"	O
parametric	B-General_Concept
"	O
model	O
all	O
the	O
parameters	O
are	O
in	O
finite-dimensional	O
parameter	O
spaces	O
;	O
</s>
<s>
a	O
model	O
is	O
"	O
non-parametric	B-General_Concept
"	O
if	O
all	O
the	O
parameters	O
are	O
in	O
infinite-dimensional	O
parameter	O
spaces	O
;	O
</s>
<s>
a	O
"	O
semi-parametric	O
"	O
model	O
contains	O
finite-dimensional	O
parameters	O
of	O
interest	O
and	O
infinite-dimensional	O
nuisance	O
parameters	O
;	O
</s>
<s>
a	O
"	O
semi-nonparametric	B-General_Concept
"	O
model	O
has	O
both	O
finite-dimensional	O
and	O
infinite-dimensional	O
unknown	O
parameters	O
of	O
interest	O
.	O
</s>
<s>
Some	O
statisticians	O
believe	O
that	O
the	O
concepts	O
"	O
parametric	B-General_Concept
"	O
,	O
"	O
non-parametric	B-General_Concept
"	O
,	O
and	O
"	O
semi-parametric	O
"	O
are	O
ambiguous	O
.	O
</s>
<s>
It	O
can	O
also	O
be	O
noted	O
that	O
the	O
set	O
of	O
all	O
probability	O
measures	O
has	O
cardinality	B-Application
of	O
continuum	O
,	O
and	O
therefore	O
it	O
is	O
possible	O
to	O
parametrize	O
any	O
model	O
at	O
all	O
by	O
a	O
single	O
number	O
in	O
(	O
0	O
,	O
1	O
)	O
interval	O
.	O
</s>
<s>
This	O
difficulty	O
can	O
be	O
avoided	O
by	O
considering	O
only	O
"	O
smooth	O
"	O
parametric	B-General_Concept
models	I-General_Concept
.	O
</s>
