Journée Mathematical Foundations of Learning Theory
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|Statistical Analysis for Rounding Data|
Zhidong Bai (National University of Singapore)
1er juin 2006
Unless the model is discrete, data rounding is unavoidable in practical measurement. However, the errors caused by rounding of data are almost ignored by all classical statistical theories. Although some pioneers have noticed this problem, few suitable approaches were proposed to deal with this error. In this work, both by simulations as well as by theoretical analysis, we demonstrate that the traditionally used sample mean and sample variance, covariance are no longer consistent nor asymptotically normal, when rounding errors are present. Also, by some concrete examples when measurements are rounded to some extent, we propose to use MLE or approximated MLE (AMLE) to estimate the parameters and discuss the properties of them and tests based on the new estimators. In particular, as an example, we shall discuss the limiting properties of the new estimator of parameters in an AR(p) model and M A(q) model when the observations are rounded.
(Joint work with Shurong Zheng and Baoxue Zhang.)