Statistical Analysis For Rounded Data

Parameter Estimation is one of three contents of statistics,in genernal, we always assume that sample obeservations come from real population f(x; θ) when making point estimation.In fact,there exists a considerable task, beacause observation data obtained in pratice always exist approximation to some extent,therefore not all real obtained sample observation values derive from f(x;θ).If the extent to approximation is very high,then we can take it as real population sample observation values.However,if the data gained in pratice exist too much error compared to real data,then we can obtain effective point estimation to population parameters only when a good statistical method does come up. In this paper,for a class of special data existng error, we bring forward estimation method of population parameters. Taking nomal population as an example,the method in the present paper can be generalized parallerally for one kind of distribution. First,we assume the sample is independent identically distributed, We consider to seek methods to estimate parameters.Moreover,we study the propoperty of estimation.In addition,we comprehend intutionistically the consistence of extimation and stand or fall of estimator by computer simulations . Second,we consider the estimation of model parameter and random error item's variance when sample observation values sequence are correlated.We take time series model AR(1) and MA(1) as examples.Because AR(1) is 2-dependent,so the farther the distance between random variables is, the smaller the correlation between is. Then we can consider the random variables, the time interval beyond some value, are approximately independent. Based on this idea, we can know the logarithm likelihood function of these approximately independent random variables. Then we can evaluate parameters by the idea of MLE. For MA(l), it is more easier, because the random variables, between which the time interval beyond 1, arc independent. Then because of the independence, we can also evaluate parameters by the idea of MLE. In the last,we estimate parameters by taking data workmen measure capability of parts as example.