Uncertain Statistical Inference Models With Imprecise Observations

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Abstract
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.
Funding Information
  • National Natural Science Foundation of China (61403360)
  • Foundation of China Scholarship Council (201504910107)
  • Special Funds for Science and Education Fusion of University of Chinese Academy of Sciences
  • Open Project of Key Laboratory of Big Data Mining and Knowledge Management of Chinese Academy of Sciences

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