Abstract
Remark 3.1. This corollary reflects the effects of the slower convergence rate of the estimated parameter a$n. This fact serves as a reminiscence of the classical Kolmogorov-Smirnov statistics problem when the underlying parame? ters are estimated; see Durbin (1976). When cxq is known, the test statistic (1.5) is still valid, however. As pointed out by the reviewer, when F ? F(x,0) involves an unknown parameter ?, one should consider Kn with F(x) being replaced by F(x,0n). When H < 1/2, it can be shown that the limit distribution of the statistic exists by means of the result of Wu (2003). The closed form of such a limit dis? tribution is rather complicated and does not possess a simple expression, however, and is not presented here.
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