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WROCŁAW UNIVERSITY
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TECHNOLOGY

Contents of PMS, Vol. 31, Fasc. 2,
pages 177 - 182
 

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 F . 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 F 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.

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