The Huber estimation for UMAR model with imprecise observations.

A nonlinear uncertain time series model was proposed which was defined as the uncertain max-autoregressive (UMAR) model. After the model is established, we pay more attention to its corresponding prediction and analysis. Before that, the estimation of unknown parameters is the top priority of a series of work. So, this paper presents the Huber estimation to estimate the unknown parameters. Then, the residual analysis and relevant prediction are discussed. Furthermore, the data of China's unemployed population, from 2002 to 2021 via the State Statistical Bureau, are used to verify the feasibility of the model and the Huber estimation. So, the relevant comparison with uncertain autoregressive (UAR) model are given to verify the practicability of the UMAR model under the Huber estimation. In addition, the relevant comparative analysis are given to present that the Huber estimation has better robustness than the least square (LS) estimation when the outliers appear. [ABSTRACT FROM AUTHOR]