Convergence of the empirical two-sample -statistics with -mixing data

k,`=1

hence

[ntu0]

n

Cov

i In,u ^Yn,i^,

i^0

^In,u^0

^Yn,i

6 n

[ntu]

α (i^0 − i) .

(2.15)

i=[ntu

1]+1 i^0

=[ntu 1]+1

1

∈^X

∈^X

K

X

X−

j

i

i

−

0

Doing the change of inded

− in the

= ^0

inner sum, it follows that

α (j)

(2.16)

n

Cov

^Yn,i^,

Yn,i

^6 n

[ntu]

[ntu0]−i

1

^i∈^In,u

i^0∈In,u0

K

i+1

i=[ntu−1

]+1 j=[ntu0−1]

−

X

X

X

X