UNBIASED ESTIMATES FOR LINEAR REGRESSION WITH ROUNDOFF
ERROR
Christopher S. Withers
Saralees Nadarajah
Abstract: We consider the linear regression model, where the residuals have zero mean and an
otherwise unspecified distribution . Suppose that least squares estimates are formed by
using rounded values of the dependent variables. We show that these are still unbiased, and
that unbiased estimates for the moments and cumulants of are given by applying
Sheppard’s corrections to their estimates.
2000 AMS Mathematics Subject Classification: Primary 62J05; Secondary
62G05.
Keywords and phrases: Grouping, least squares, regression, round-off error, Sheppard’s
corrections, unbiased.