<s>
Nonparametric	B-General_Concept
statistics	I-General_Concept
is	O
the	O
branch	O
of	O
statistics	O
that	O
is	O
not	O
based	O
solely	O
on	O
parametrized	O
families	O
of	O
probability	O
distributions	O
(	O
common	O
examples	O
of	O
parameters	O
are	O
the	O
mean	O
and	O
variance	O
)	O
.	O
</s>
<s>
Nonparametric	B-General_Concept
statistics	I-General_Concept
is	O
based	O
on	O
either	O
being	O
distribution-free	B-General_Concept
or	O
having	O
a	O
specified	O
distribution	O
but	O
with	O
the	O
distribution	O
's	O
parameters	O
unspecified	O
.	O
</s>
<s>
Nonparametric	B-General_Concept
statistics	I-General_Concept
includes	O
both	O
descriptive	B-General_Concept
statistics	I-General_Concept
and	O
statistical	O
inference	O
.	O
</s>
<s>
Nonparametric	B-General_Concept
tests	I-General_Concept
are	O
often	O
used	O
when	O
the	O
assumptions	O
of	O
parametric	B-General_Concept
tests	I-General_Concept
are	O
violated	O
.	O
</s>
<s>
The	O
term	O
"	O
nonparametric	B-General_Concept
statistics	I-General_Concept
"	O
has	O
been	O
imprecisely	O
defined	O
in	O
the	O
following	O
two	O
ways	O
,	O
among	O
others	O
:	O
</s>
<s>
Non-parametric	B-General_Concept
methods	I-General_Concept
are	O
widely	O
used	O
for	O
studying	O
populations	O
that	O
take	O
on	O
a	O
ranked	O
order	O
(	O
such	O
as	O
movie	O
reviews	O
receiving	O
one	O
to	O
four	O
stars	O
)	O
.	O
</s>
<s>
The	O
use	O
of	O
non-parametric	B-General_Concept
methods	I-General_Concept
may	O
be	O
necessary	O
when	O
data	O
have	O
a	O
ranking	O
but	O
no	O
clear	O
numerical	O
interpretation	O
,	O
such	O
as	O
when	O
assessing	O
preferences	O
.	O
</s>
<s>
In	O
terms	O
of	O
levels	O
of	O
measurement	O
,	O
non-parametric	B-General_Concept
methods	I-General_Concept
result	O
in	O
ordinal	B-General_Concept
data	I-General_Concept
.	O
</s>
<s>
As	O
non-parametric	B-General_Concept
methods	I-General_Concept
make	O
fewer	O
assumptions	O
,	O
their	O
applicability	O
is	O
much	O
wider	O
than	O
the	O
corresponding	O
parametric	B-General_Concept
methods	O
.	O
</s>
<s>
Also	O
,	O
due	O
to	O
the	O
reliance	O
on	O
fewer	O
assumptions	O
,	O
non-parametric	B-General_Concept
methods	I-General_Concept
are	O
more	O
robust	O
.	O
</s>
<s>
Another	O
justification	O
for	O
the	O
use	O
of	O
non-parametric	B-General_Concept
methods	I-General_Concept
is	O
simplicity	O
.	O
</s>
<s>
In	O
certain	O
cases	O
,	O
even	O
when	O
the	O
use	O
of	O
parametric	B-General_Concept
methods	O
is	O
justified	O
,	O
non-parametric	B-General_Concept
methods	I-General_Concept
may	O
be	O
easier	O
to	O
use	O
.	O
</s>
<s>
Due	O
both	O
to	O
this	O
simplicity	O
and	O
to	O
their	O
greater	O
robustness	O
,	O
non-parametric	B-General_Concept
methods	I-General_Concept
are	O
seen	O
by	O
some	O
statisticians	O
as	O
leaving	O
less	O
room	O
for	O
improper	O
use	O
and	O
misunderstanding	O
.	O
</s>
<s>
The	O
wider	O
applicability	O
and	O
increased	O
robustness	O
of	O
non-parametric	B-General_Concept
tests	I-General_Concept
comes	O
at	O
a	O
cost	O
:	O
in	O
cases	O
where	O
a	O
parametric	B-General_Concept
test	I-General_Concept
would	O
be	O
appropriate	O
,	O
non-parametric	B-General_Concept
tests	I-General_Concept
have	O
less	O
power	B-General_Concept
.	O
</s>
<s>
Non-parametric	B-General_Concept
models	I-General_Concept
differ	O
from	O
parametric	B-General_Concept
models	O
in	O
that	O
the	O
model	O
structure	O
is	O
not	O
specified	O
a	O
priori	O
but	O
is	O
instead	O
determined	O
from	O
data	O
.	O
</s>
<s>
The	O
term	O
non-parametric	B-General_Concept
is	O
not	O
meant	O
to	O
imply	O
that	O
such	O
models	O
completely	O
lack	O
parameters	O
but	O
that	O
the	O
number	O
and	O
nature	O
of	O
the	O
parameters	O
are	O
flexible	O
and	O
not	O
fixed	O
in	O
advance	O
.	O
</s>
<s>
A	O
histogram	B-Algorithm
is	O
a	O
simple	O
nonparametric	B-General_Concept
estimate	O
of	O
a	O
probability	O
distribution	O
.	O
</s>
<s>
Kernel	B-General_Concept
density	I-General_Concept
estimation	I-General_Concept
is	O
another	O
method	O
to	O
estimate	O
a	O
probability	O
distribution	O
.	O
</s>
<s>
Nonparametric	B-General_Concept
regression	O
and	O
semiparametric	B-General_Concept
regression	I-General_Concept
methods	O
have	O
been	O
developed	O
based	O
on	O
kernels	O
,	O
splines	B-Algorithm
,	O
and	O
wavelets	O
.	O
</s>
<s>
KNNs	B-General_Concept
classify	O
the	O
unseen	O
instance	O
based	O
on	O
the	O
K	O
points	O
in	O
the	O
training	O
set	O
which	O
are	O
nearest	O
to	O
it	O
.	O
</s>
<s>
A	O
support	B-Algorithm
vector	I-Algorithm
machine	I-Algorithm
(	O
with	O
a	O
Gaussian	O
kernel	O
)	O
is	O
a	O
nonparametric	B-General_Concept
large-margin	O
classifier	O
.	O
</s>
<s>
Non-parametric	B-General_Concept
(	O
or	O
distribution-free	B-General_Concept
)	O
inferential	O
statistical	O
methods	O
are	O
mathematical	O
procedures	O
for	O
statistical	O
hypothesis	O
testing	O
which	O
,	O
unlike	O
parametric	B-General_Concept
statistics	I-General_Concept
,	O
make	O
no	O
assumptions	O
about	O
the	O
probability	O
distributions	O
of	O
the	O
variables	O
being	O
assessed	O
.	O
</s>
<s>
Early	O
nonparametric	B-General_Concept
statistics	I-General_Concept
include	O
the	O
median	O
(	O
13th	O
century	O
or	O
earlier	O
,	O
use	O
in	O
estimation	O
by	O
Edward	O
Wright	O
,	O
1599	O
;	O
see	O
)	O
and	O
the	O
sign	B-General_Concept
test	I-General_Concept
by	O
John	O
Arbuthnot	O
(	O
1710	O
)	O
in	O
analyzing	O
the	O
human	O
sex	O
ratio	O
at	O
birth	O
(	O
see	O
)	O
.	O
</s>
