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 language | English |
|---|---|
| Pages (from-to) | 287-292 |
| Number of pages | 6 |
| Journal | Journal of Statistical Planning and Inference |
| Volume | 141 |
| Issue number | 1 |
| DOIs | |
| Publication status | Published - 2011 Jan |
| Externally published | Yes |
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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 journal › Article
}
TY - JOUR
T1 - On Z-estimation by rounded data
AU - Nishiyama, Yoichi
PY - 2011/1
Y1 - 2011/1
N2 - 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.
AB - 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.
KW - Discretized observation
KW - Estimating function
KW - Rounded data
UR - http://www.scopus.com/inward/record.url?scp=77956291874&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=77956291874&partnerID=8YFLogxK
U2 - 10.1016/j.jspi.2010.06.005
DO - 10.1016/j.jspi.2010.06.005
M3 - Article
AN - SCOPUS:77956291874
VL - 141
SP - 287
EP - 292
JO - Journal of Statistical Planning and Inference
JF - Journal of Statistical Planning and Inference
SN - 0378-3758
IS - 1
ER -