论文标题
参数分布家族的离散混合物表示：几何和统计数据
Discrete mixture representations of parametric distribution families: geometry and statistics
论文作者
论文摘要
我们调查了离散混合物表示的存在和属性$p_θ= \ sum_ {i \ in e}w_θ（i）\，q_i $，q_i $，对于给定的家族$p_θ$，$θ\inθ$，概率度量。非中央卡方分布提供了一个经典的例子。我们获得了有关问题的几何和统计方面的存在结果和结果，后者包括Fisher信息的丢失，Rao-Blackwellization，渐近效率和混合概率的非参数最大似然估计。
We investigate existence and properties of discrete mixture representations $P_θ=\sum_{i\in E} w_θ(i) \, Q_i$ for a given family $P_θ$, $θ\inΘ$, of probability measures. The noncentral chi-squared distributions provide a classical example. We obtain existence results and results about geometric and statistical aspects of the problem, the latter including loss of Fisher information, Rao-Blackwellization, asymptotic efficiency and nonparametric maximum likelihood estimation of the mixing probabilities.
