Question: What is the characteristic function of the limiting random variable W of Theorem 14.5.1? As a special case, show that the characteristic function of the

What is the characteristic function of the limiting random variable W of Theorem 14.5.1? As a special case, show that the characteristic function of the limiting null distribution of the Cram´er-von Mises statistic is given by

ζ(t) = ∞

j=1

(1 − 2t

πj )

−1/2 .

(Note this characteristic function was inverted by Smirnov; see Durbin (1973), p.32.)

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