We derive quantitative bounds on the rate of convergence in $L^1$ Wasserstein distance of general M-estimators, with an almost sharp (up to a logarithmic term) behavior in the number of observations. We focus on situations where the estimator does not have an explicit expression as a function of the data. The general method may be applied even in situations where the observations are not independent. Our main application is a rate of convergence for cross validation estimation of covariance parameters of Gaussian processes.

翻译：我们从一般测算员的瓦塞斯坦距离(瓦塞斯坦)的趋同率中得出数量界限,在观测数量上几乎具有尖锐(直至对数术语)的行为。我们侧重于估计员没有作为数据函数的明确表达方式的情况。一般方法即使在观测不独立的情况下也可以适用。我们的主要应用是,对高斯进程共变参数进行交叉验证估计的趋同率。