The Impact Of Statistical Inference Based On The Rounded Data

When we are performing statistical inference, we often take the observations as real data to carry on the traditional statistical inference. Because the precision of measuring instruments, pre-cision of the recording data and precision of the medium, which is used to storage the data. Under these different factors, the observations are often the rounded data. Among the many kinds of rounded data, the rounded data is more universal and better rationality. When used the rounding data to carry on the traditional statistical inference, the rounding error could pass to the estimation, which affect the work of the estimation. the effect on hypothesis testing may have a great impact. Moment estimation is the more important estimated method in the parameter estimations, distri-bution function estimation is basic estimation on the non-parameter estimation, according to these tow types of estimations, to research the impact from the rounded data is very necessary.Under the tow cases, which the rounded data of random variable has the finite values or the infinite number values, firstly in this paper systematically studied the relationship between the rounded variable moments and the original variable moments. Through the research, we found that there have some functional relations between the rounding variables moments and the origi-nal variable moments. Through the simulation, the estimations of the rounded data have not the consistency in many situations. We can see this influence is very serious. Based on this influence from the rounded data, this paper presented that the moment estimations of the rounded data have the sufficient conditions of the unbiasedness and consistency. Through the researching the influ-ence of the rounded data about the distribution function estimation, we found that the distribution function estimation, which gets form the rounded data, has no unbiased character,the gradual unbiased character and consistency. In this paper, we made the empirical distribution function of the rounded data into the following form: Then G*n (x) has the point wise asymptotically unbiased character.