Empirical Likelihood Method For The Rounded Data

Due to the influence of measuring instrument storage medium, the rounding data often ap-pears in actual life. When datas are rounded, classical statistical inference will causes considerable problem, which is not content with excellent properties of the original any longer, such as unbi-asedness, consistency property. The errors caused by rounding will be passed to the statistical inference, and then that will reduce the accurate precision of statistical inference. Therefore, we urgently need to find a new statistical methods or to adjust the existing classical method on the rounded data. On the other hand, the empirical likelihood is one of the popular non-parameter statistics method in recent years, which is similar to the large sample properties of parameter like-lihood, and has many outstanding advantage. Therefore, it is strong theory and application value to research the rounded data by empirical likelihood methods.This thesis discusses empirical likelihood method for the rounded data with Owen (1988) empirical likelihood thought and Qin and Lawless (1994)’s semiparametric model. Due to round-ing influence, it makes originally continuous random variables into discrete random variables. To make empirical likelihood use smoothly, the paper adjusts the rounding datas at first, and makes the adjusted random variable with continuous distribution function. The adjusted random variables can be considered as a kind of approximate of original variables; Therefore, then we analysis the relationship the corresponding digital characteristics and the distribution function between the ad-justed random variables and the original variables; Then we use empirical likelihood method to discuss statistical inference method for the rounded data, and give the corresponding parameter es-timation and the statistical properties; Finally simulating on the above analysis, and the simulation results show that the estimate of the adjusted is better than the estimate which isn’t adjusted.This paper characteristic mainly reflects in the following aspects:1. This paper got the new data by adjusting the rounded data. We discussed the moment and distribution function of the data, got the adjustment empirical likelihood ratio function, and discussed the function and the asymptotic properties of its corresponding parameters estimates, such as asymptotic distribution, consistency property.2. Adjusted data is a better approximation to the rounded data, and it is more important to use classic or existing relatively mature method as the adjusted data has continuous distribution.