We introduce a quantitatively weak version of sufficient statistics such that the Fisher metric of the induced parametrized measure model is bi-Lipschitz equivalent to the Fisher metric of the original model. We characterize such statistics in terms of the conditional probability or by the existence of a certain decomposition of the density function in a way similar to characterizations of due to Ay-Jost-L\^e-Schwachh\"ofer and Fisher-Neyman for sufficient statistics.

翻译：我们引入了充分统计量的一种量化弱化版本，使得诱导参数化测度模型的Fisher度量与原模型的Fisher度量双Lipschitz等价。我们通过条件概率或密度函数存在某种分解的方式刻画了此类统计量，其刻画方式类似于Ay-Jost-Lê-Schwachhöfer以及Fisher-Neyman对充分统计量的刻画。