Estimation of unknown parameters in uncertainty distribution via the least absolute deviation principle and its application in uncertain statistics

Estimating the unknown parameters within the uncertainty distribution based on observational data has always been one of the key research focuses in the field of uncertain statistics. To address the issue of imbalanced weights of outliers caused by the least squares estimation method, this paper proposes a least absolute deviation estimation based on uncertainty distribution by applying the least absolute deviation principle to minimize the deviations of the empirical distribution and the uncertainty distribution. To illustrate the proposed method more specifically, this paper also presents the least absolute deviation estimations for normal uncertainty distribution and linear uncertainty distribution, and applies them to the residual analysis of uncertain regression analysis and uncertain time series analysis. Finally, this paper provides several real data examples to illustrate the above research results.