No. 1101

Title:

Two sample problem for rounded data

Author(s):

Nishiyama, Yoichi (The Institute of Statistical Mathematics)

Key words:

Discretized observation, empirical process, two sample problem, invariance principle.

Abstract:

    This paper deals with two sample problem for rounded data in the i.i.d. model. It is well known that under the null hypothesis two sample Kolmogorov-Smirnov statistic without rounding converges in distribution to the supremum of a standard Brownian bridge. We establish that a natural statistic of the Kolmogorov-Smirnov type based on the rounded data converges in distribution to the same limit as the full observation case. Our result is based on ``Donsker's theorem for discretized data'' given by Nishiyama (2008, J. Japan Statist. Soc.).