论文标题
部分可观测时空混沌系统的无模型预测
Novel Closed-form Point Estimators for the Beta Distribution
论文作者
论文摘要
在本文中，提出并研究了β分布的新型闭合点估计量。第一个估计量是Pearson瞬间方法的修改版本。潜在的想法是涉及到足够的统计数据，即在矩估计方程中的对数矩，并同时求解矩方程的混合类型。第二个估计量基于Fisher的可能性原理的近似。这个想法是解决从广义beta分布的对数可能性函数得出的两个分数方程。两个结果的估计量均处于封闭形式，非常一致且渐近地正常。此外，通过大量的模拟，所提出的估计器被证明可以非常接近小样本中的ML估计量，并且它们的表现明显优于矩估计器。
In this paper, novel closed-form point estimators of the beta distribution are proposed and investigated. The first estimators are a modified version of Pearson's method of moments. The underlying idea is to involve the sufficient statistics, i.e., log-moments in the moment estimation equations and solve the mixed type of moment equations simultaneously. The second estimators are based on an approximation to Fisher's likelihood principle. The idea is to solve two score equations derived from the log-likelihood function of generalized beta distributions. Both two resulted estimators are in closed forms, strongly consistent and asymptotically normal. In addition, through extensive simulations, the proposed estimators are shown to perform very close to the ML estimators in both small and large samples, and they significantly outperform the moment estimators.
