A statistic on a statistical model is sufficient if it has no information loss, namely, the Fisher metric of the induced model coincides with that of the original model due to Kullback and Ay-Jost-L\^e-Schwachh\"ofer. We introduce a quantitatively weak version of sufficient statistics such that the Fisher metric of the induced model is bi-Lipschitz equivalent to that 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 sufficient statistics due to Fisher-Neyman and Ay-Jost-L\^e-Schwachh\"ofer.

翻译：在统计模型中，若某统计量无信息损失，即由Kullback与Ay-Jost-Lê-Schwachhöfer所指出的诱导模型的Fisher度量与原模型一致，则该统计量是充分的。我们引入充分统计量的定量弱化版本，使得诱导模型的Fisher度量与原模型的Fisher度量双Lipschitz等价。我们通过条件概率或以类似于Fisher-Neyman和Ay-Jost-Lê-Schwachhöfer对充分统计量的刻画方式，借助密度函数的特定分解存在性，来表征此类统计量。