Uncertain Statistical Inference Models With Imprecise Observations

The observations of some samples from the population of a probability density function with unknown parameters are usually imprecise due to various reasons. By employing uncertain variables to model these imprecise observations, this paper proposes an interdiscipline called the uncertain statistical inference, which is composed of statistical inference and uncertainty theory. It presents three types of statistic inference problems with imprecise observations that are the point estimation, the hypothesis test, and the interval estimation. Then, it proposes a method of moments and a method of likelihood function (maximum likelihood estimation) for the first problem, and a method of likelihood ratio function for the other two problems.