On Z-estimation by rounded data

Research output: Contribution to journalArticle

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 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
Volume141
Issue number1
DOIs
Publication statusPublished - 2011 Jan
Externally publishedYes

Fingerprint

Rounding error
Sample Size
Discretization
Tend
Continuous Distributions
Random variables
Random variable
Infinity
Statistics
Mesh
Sufficient Conditions
Zero
Sample size
Context
Form

Keywords

  • Discretized observation
  • Estimating function
  • Rounded data

ASJC Scopus subject areas

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

Cite this

On Z-estimation by rounded data. / Nishiyama, Yoichi.

In: Journal of Statistical Planning and Inference, Vol. 141, No. 1, 01.2011, p. 287-292.

Research output: Contribution to journalArticle

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