No. 1091

Title:

On Z-estimation by rounded data

Author(s):

Nishiyama, Yoichi (The Institute of Statistical Mathematics)

Key words:

Discretized observation, rounded data, estimating function.

Abstract:

    It is often assumed in statistics that the random variables under consideration come from a continuous distribution. However, real data is always given in a rounded (discretized) form. The rounding errors become serious when the sample size is large. In this paper, we consider the situation where the {\em mesh} of discretization tends to zero as the sample size tends to infinity, and give some sets of sufficient conditions under which the rounding errors can be asymptotically ignored, in the context of $ Z $-estimation. It is theoretically proved that the mid-point discretization is preferable.