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

n1/2

n3/2

Therefore, defining

ξ^o (s, t) :=

1

[nt] a

(X )+

[nt]

n

b

(X ) + 2m [nt]^2

and

(2.33)

n

X

s

i

X

s

j

s

n

1/2

i=1

n

3/2

j=1

n

3/2

ξ^∗ (s, t) :=

[nt] ^[^nt^]

a

(X ) + ^[^nt^]

[nt]

b

(X ) + 2m

[nt] ,

(2.34)

n

X

s

i

X

s

j

s

n

3/2

i=1

n

3/2

j=1