Title: On the attainment of the Wasserstein--Cramer--Rao lower bound Show Chinese title

Title: 关于Wasserstein--Cramer--Rao下界的有效性

Abstract: Recently, a Wasserstein analogue of the Cramer--Rao inequality has been developed using the Wasserstein information matrix (Otto metric). This inequality provides a lower bound on the Wasserstein variance of an estimator, which quantifies its robustness against additive noise. In this study, we investigate conditions for an estimator to attain the Wasserstein--Cramer--Rao lower bound (asymptotically), which we call the (asymptotic) Wasserstein efficiency. We show a condition under which Wasserstein efficient estimators exist for one-parameter statistical models. This condition corresponds to a recently proposed Wasserstein analogue of one-parameter exponential families (e-geodesics). We also show that the Wasserstein estimator, a Wasserstein analogue of the maximum likelihood estimator based on the Wasserstein score function, is asymptotically Wasserstein efficient in location-scale families. Show Chinese abstract

Abstract: 最近，利用Wasserstein信息矩阵（Otto度量）开发了Cramer--Rao不等式的Wasserstein类似形式。 这个不等式提供了估计量的Wasserstein方差的下界，这量化了其对抗加性噪声的鲁棒性。 在本研究中，我们研究了估计量达到Wasserstein--Cramer--Rao下界（渐近地）的条件，我们称之为（渐近）Wasserstein效率。 我们证明了一个条件，在该条件下，对于单参数统计模型存在Wasserstein有效的估计量。 该条件对应于最近提出的单参数指数族的Wasserstein类似形式（e-geodesics）。 我们还证明了Wasserstein估计量，即基于Wasserstein评分函数的极大似然估计量的Wasserstein类似形式，在位置尺度族中是渐近的Wasserstein有效的。