Bounds in L^1 Wasserstein distance on the normal approximation of general M-estimators
share
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.
READ FULL TEXT