## Symmetric and asymmetric rounding: a review and some new results

Schneeweiss, H., Komlos, J., Ahmad, A. S.
(2010)
*Symmetric and asymmetric rounding: a review and some new results.*
ASTA-ADVANCES IN STATISTICAL ANALYSIS, 94 (3).
pp. 247-271.
ISSN 1863-8171

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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.

Item Type: | Review Article |
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All Authors: | Schneeweiss, H., Komlos, J., Ahmad, A. S. |

Uncontrolled Keywords: | Simple rounding; Asymmetric rounding; Euler-Maclaurin; Moments; Sheppard's correction; Maximum likelihood;MAXIMUM-LIKELIHOOD-ESTIMATION; GROUPED DATA; SHEPPARDS CORRECTIONS; INTERVAL ESTIMATION; DENSITY-ESTIMATION; COARSE DATA; VARIABLES; QUANTIZATION; REGRESSION; MODEL |

Research teams: | Closed research groups > Other closed groups |

Depositing User: | Users 10 not found. |

Date Deposited: | 22 Oct 2010 08:09 |

Last Modified: | 02 Sep 2011 15:10 |

URI: | http://publications.icr.ac.uk/id/eprint/9982 |

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