论文标题
广义的Fisher-Darmois-Koopman-Pitman定理和Rao-Blackwell类型估计器用于Power-Laws发行量
Generalized Fisher-Darmois-Koopman-Pitman Theorem and Rao-Blackwell Type Estimators for Power-Law Distributions
论文作者
论文摘要
本文概括了超出最大可能性的估计问题的充分性概念。特别是，我们考虑基于Jones等人的估计问题。和Basu等。在基于距离的鲁棒推理方法中流行的可能性函数。我们首先表征了相对于这些可能性功能，这些概率分布始终具有固定数量的足够数量的足够统计数据（与样本量无关）。这些分布是通常的指数家庭的幂律扩展，并包含学生分布作为特殊情况。然后，我们扩展了最小的足够统计数据的概念，并为这些幂律家庭计算它。最后，我们建立了一个Rao-Blackwell-type定理，用于为幂律家庭找到最佳的估计器。这有助于我们为幂律家庭建立Cramér-rao型的下限。
This paper generalizes the notion of sufficiency for estimation problems beyond maximum likelihood. In particular, we consider estimation problems based on Jones et al. and Basu et al. likelihood functions that are popular among distance-based robust inference methods. We first characterize the probability distributions that always have a fixed number of sufficient statistics (independent of sample size) with respect to these likelihood functions. These distributions are power-law extensions of the usual exponential family and contain Student distributions as a special case. We then extend the notion of minimal sufficient statistics and compute it for these power-law families. Finally, we establish a Rao-Blackwell-type theorem for finding the best estimators for a power-law family. This helps us establish Cramér-Rao-type lower bounds for power-law families.
