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

and using again (2.41), we derive (2.35).

11
Let us show (2.36). This time, we have to control the increments in the first variable. For s, s⁰, t ∈ [0, 1] such that s⁰ − s > 1/n,

ξn (s^0, t)

ξn (s, t) 6 ^n ^−3/^[2

]

(as (Xi)

as0 (Xi) + ms0

ms)

|

−

|

nt

[nt]

−

−

n

i=1

^X

[nt]

n

+

(bs (Xi)

−

bs0 (Xi) + bs0

−

bs)

. (2.45)

n

3/2

i=[nt]+1