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


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Z

R =

06t61

Z[−R,R]

W 0 (s, t)2(s)).

















































(2.110)














































sup












































































Assumption 1 follows from the continuous mapping theorem applied with the functional
















ΦR

(







) =

06t61

Z[−R,R]



















































































































(2.111)































f
















sup






















f (s, t)2(s) .











































In order to show that assumptions 2 and 3 hold, it suffices to show that































R→+∞ n>1

ZR\[−R,R] E

06t61




n

(s, t)2

























( )=0






















(2.112)













lim

sup











































sup

e
























s








































and




R→+∞ n>1







ZR\[−R,R] E

06t61










(










)































(







) = 0











































n

s, t


















s




.






















(2.113)













lim

sup

















































sup

e0








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