No. 1068

Title:

Donsker's theorem for discretized data

Author(s):

Nishiyama, Yoichi (The Institute of Statistical Mathematics)

Key words:

Discretized observation, empirical process, goodness of fit test, invariance principle.

Abstract:

    In the Kolmogorov-Smirnov theorem, the underlying distribution is assumed to be a continuous distribution. On the other hand, the 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 discreteized data.