Analysis Of Rounded Data In Statistics

There are many inevitable factors causing the data being rounded in statisticalpractice, such as the precision of measuring instruments and/or the confinement of therecord or storage mechanism. Especially for the data from continuous distribution, thedata must be recorded in rounded format. Although the data rounding is omnipresentin the measurements of continuous variables and the rounding errors have certainlyimpact to statistical inferences, it has been ignored in almost all statistical procedures.As a matter of fact, rounding errors have a considerable impact on statistical inferences,especially when the data size is large. This thesis focus on discussing the in?uence ofrounding error in statistical inferences, and paying e?ort to find a method to correctthe rounding error.The finite normal mixture model is a class of very important statistical models.It has been employed in many applied statistical problems, such as bioinformatics,remote sensing applications, pharmaceutical studies, modeling for economics and fi-nancial problems, etc. In this thesis, we investigate the statistical impacts of roundingerrors to the finite normal mixture model with a known number of components, anddevelop a new estimation method to obtain consistent and asymptotically normal es-timates for the unknown parameters based on rounded data drawn from this kind ofmodels.Measurement error models are concerned with inference on regression coe?-cients for a response variable Y in terms of an explanatory variable x, in cases where xis not measured accurately on all subjects, but information on x is available through therecord of an imperfect surrogate X. It is well known that ignoring the measurement er-rors can lead to serious errors in statistical inferences when considering the regressionof Y on X. In this paper, we revisit the measurement error model when both the de-pendent and explanatory variables further have rounding errors. Additionally, the useof a normal mixture distribution for the explanatory variables in measurement errorregression is in line with recent developments. This paper proposes a new method for estimating the model parameters. The estimates obtained by the new method possessthe properties of consistence and asymptotical normality.