A modified uncertain maximum likelihood estimation with applications in uncertain statistics

AbstractIn uncertain statistics, the uncertain maximum likelihood estimation is a method of estimating the values of unknown parameters of an uncertain statistical model that make the observed data most likely. However, the observed data obtained in practice usually contain outliers. In order to eliminate the influence of outliers when estimating unknown parameters, this article modifies the uncertain maximum likelihood estimation. Following that, the modified uncertain maximum likelihood estimation is applied to uncertain regression analysis, uncertain time series analysis, and uncertain differential equation. Finally, some real-world examples are provided to illustrate the modified uncertain maximum likelihood estimation.KEYWORDS: Uncertainty theorymaximum likelihood estimationuncertain regression analysisuncertain time series analysisuncertain differential equation Disclosure statementNo potential conflict of interest was reported by the authors.Notes1 MATLAB R2022a, 9.12.0.1884302, maci64, Optimization Toolbox, "fminsearch" function.Additional informationFundingThis work was supported by National Natural Science Foundation of China Grant No.61873329.