On Z-estimation by rounded data

Yoichi Nishiyama*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


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 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.

Original languageEnglish
Pages (from-to)287-292
Number of pages6
JournalJournal of Statistical Planning and Inference
Issue number1
Publication statusPublished - 2011 Jan 1
Externally publishedYes


  • Discretized observation
  • Estimating function
  • Rounded data

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics


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