Donsker's Theorem for Discretized Data

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  • Nishiyama Yoichi
    The Institute of Statistical Mathematics, 4-6-7 Minami-Azabu, Minato-ku, Tokyo 106-8569, Japan.

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In the Kolmogorov-Smirnov theorem, the underlying distribution is assumed to be a continuous distribution. On the other hand, real data in practice is always given in a discretized (rounded) form. In this paper we establish a Donsker type theorem in the fashion of the modern empirical process theory to obtain a (right) Kolmogorov-Smirnov test for discretized data.

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