Parameter Estimation From Rounded Data

In standard statistical analyses,data are assumed to be essentially.But indeed they are often obtained from a relatively crude gaging method and are thus intrinsically " rounded" to some nearest unit.For example,because of the precision of the measuring device, the time between trades is recorded to the nearest second.If we ignore "rounded" ,the eatimator which we obtain don't satisfy the consistency.The famous analysis of Sheppard provides approximate relationships between the moments of a continuous distribution and those of a corresponding approximating discrete distribution.But this correction need very strick condition about distribution.So we seek another method to solve this problem.In particular,we focus discussion on joint confidence sets of the parameter mean and variance when a rounded sample comes from the normal distribution with both parameters unknown. The traditional method and a rounded-data likelihood-based method are compared.We find that the likelihood-based method provides a reliable means of estimating mean and variance.