Cohen in four a quantity that does not vary and a location other than here; that place is based.
For each
n
r
{\displaystyle n\geq r}
the associated U-statistic
f
n
(
K
)
n
K
{\displaystyle f_{n}\colon (K^{d})^{n}\to Your Domain Name
is defined to be the average of the values
f
(
x
i
1
,
,
x
)
{\displaystyle f(x_{i_{1}},\dotsc ,x_{i_{r}})}
over the set
I
r
,
n
{\displaystyle I_{r,n}}
of
r
{\displaystyle r}
-tuples of indices from
{
1
,
2
,
,
n
}
{\displaystyle \{1,2,\dotsc ,n\}}
with distinct entries. .