AStA Advances in Statistical Analysis

, Volume 94, Issue 3, pp 247–271 | Cite as

Symmetric and asymmetric rounding: a review and some new results

Original Paper
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Abstract

Using rounded data to estimate moments and regression coefficients typically biases the estimates. We explore the bias-inducing effects of rounding, thereby reviewing widely dispersed and often half forgotten results in the literature. Under appropriate conditions, these effects can be approximately rectified by versions of Sheppard’s correction formula. We discuss the conditions under which these approximations are valid and also investigate the efficiency loss caused by rounding. The rounding error, which corresponds to the measurement error of a measurement error model, has a marginal distribution, which can be approximated by the uniform distribution, but is not independent of the true value. In order to take account of rounding preferences (heaping), we generalize the concept of simple rounding to that of asymmetric rounding and consider its effect on the mean and variance of a distribution.

Keywords

Simple rounding Asymmetric rounding Euler–Maclaurin Moments Sheppard’s correction Maximum likelihood 
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Copyright information

© Springer-Verlag 2010

Authors and Affiliations

  1. 1.Department of StatisticsUniversity of Munich LMUMunichGermany
  2. 2.Department of Economic HistoryUniversity of Munich LMUMunichGermany
  3. 3.Institute of Cancer ResearchLondonUK

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