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.

中文翻译：

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具有不精确观察的不确定统计推理模型

由于各种原因，对未知参数的概率密度函数总体中的一些样本的观察通常是不精确的。通过使用不确定变量对这些不精确的观察进行建模，本文提出了一个交叉学科，称为不确定统计推理，它由统计推理和不确定性理论组成。它提出了三种类型的具有不精确观测值的统计推断问题，即点估计、假设检验和区间估计。然后，针对第一个问题提出矩量法和似然函数法（最大似然估计），针对其他两个问题提出似然比函数法。