Summary
The Kolmogorov-Smirnov test for regression alternatives is defined in Section 3, where an artificial numerical example is also given. The limiting distribution is derived in Section 4 by means of techniques developed in Section 1 (conditions for convergence in distribution in C [0, 1]) and Section 2 (extension of a Kolmogorov inequality to the case of sampling without replacement from a finite population). The auxiliary results just mentioned also offer some interest in their own right.
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Hájek, J. (1965). Extension of the Kolmogorov-Smirnov Test to Regression Alternatives. In: Neyman, J., Le Cam, L.M. (eds) Bernoulli 1713 Bayes 1763 Laplace 1813. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-49750-6_6
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