Please use this identifier to cite or link to this item: https://doi.org/10.1007/s11425-010-4010-y
Title: Revisit of Sheppard corrections in linear regression
Authors: Liu, T.Q.
Zhang, B.X.
Hu, G.R.
Bai, Z.D. 
Keywords: Asymptotic normality
Consistency
Linear regression model
Rounded data
Two-stage estimates
Issue Date: 2010
Citation: Liu, T.Q., Zhang, B.X., Hu, G.R., Bai, Z.D. (2010). Revisit of Sheppard corrections in linear regression. Science China Mathematics 53 (6) : 1435-1451. ScholarBank@NUS Repository. https://doi.org/10.1007/s11425-010-4010-y
Abstract: Dempster and Rubin (D&R) in their JRSSB paper considered the statistical error caused by data rounding in a linear regression model and compared the Sheppard correction, BRB correction and the ordinary LSE by simulations. Some asymptotic results when the rounding scale tends to 0 were also presented. In a previous research, we found that the ordinary sample variance of rounded data from normal populations is always inconsistent while the sample mean of rounded data is consistent if and only if the true mean is a multiple of the half rounding scale. In the light of these results, in this paper we further investigate the rounding errors in linear regressions. We notice that these results form the basic reasons that the Sheppard corrections perform better than other methods in D&R examples and their conclusion in general cases is incorrect. Examples in which the Sheppard correction works worse than the BRB correction are also given. Furthermore, we propose a new approach to estimate the parameters, called "two-stage estimator", and establish the consistency and asymptotic normality of the new estimators. © Science China Press and Springer-Verlag Berlin Heidelberg 2010.
Source Title: Science China Mathematics
URI: http://scholarbank.nus.edu.sg/handle/10635/105333
ISSN: 16747283
DOI: 10.1007/s11425-010-4010-y
Appears in Collections:Staff Publications

Show full item record
Files in This Item:
There are no files associated with this item.

SCOPUSTM   
Citations

2
checked on Jan 13, 2022

Page view(s)

88
checked on Jan 13, 2022

Google ScholarTM

Check

Altmetric


Items in DSpace are protected by copyright, with all rights reserved, unless otherwise indicated.