Revisit of Sheppard corrections in linear regression  

作　　者：LIU TianQing1,ZHANG BaoXue1,HU GuoRong1 & BAI ZhiDong1,2,1Key Laboratory for Applied Statistics of MOE and School of Mathematics and Statistics,Northeast Normal University,Changchun 130024,China 2Department of Statistics and Applied Probability,National University of Singapore,Singapore 117543,Singapore 

出　　处：《Science China Mathematics》2010年第6期1435-1451,共17页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant No.10871037);Program for New Century Excellent Talents in University(Grant No.NCET-09-0284);supported by National Natural Science Foundation of China (Grant No.10871036);the NUS Grant (Grant No.R-155-000-079-112)

摘　　要：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.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.

关 键 词：ASYMPTOTIC NORMALITY consistency linear regression model rounded data TWO-STAGE ESTIMATES 

分 类 号：O212.1[理学—概率论与数理统计]