Abstract Parameter estimation is a critical problem for the uncertain differential equation to achieve its full potential. Based on the Liu process’s properties and the difference form of the uncertain differential equation, the existing method of moments is intuitive but sometimes has no solution. As a result, this method is invalid and alternative ways are needed to estimate unknown parameters in the uncertain differential equation. Motivated by this, this paper proposes the generalized moment estimation which is the optimal solution of a minimization problem. Generalized moment estimation is equivalent to moment estimation when moment estimation exists, and still works well when moment estimation is invalid. Numerical examples and an empirical analysis on the interest rate illustrate the rationality and superiority of the generalized moment estimation.

中文翻译：

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不确定微分方程的广义矩估计

摘要 参数估计是不确定微分方程充分发挥其潜力的关键问题。基于刘过程的性质和不确定微分方程的差分形式，现有的矩量法直观但有时无解。因此，该方法是无效的，需要替代方法来估计不确定微分方程中的未知参数。受此启发，本文提出了广义矩估计，这是最小化问题的最优解。广义矩估计等价于矩估计存在时的矩估计，当矩估计无效时仍然有效。