The empirical cost of optimal incomplete transportation (Q378795)

The authors consider the problem of optimal incomplete transportation. They establish exact rates of convergence for empirical versions of this problem. The incomplete \(L_p\)-Wasserstein distance between the empirical measure and the underlying uniform measures on \([0,1]^d\) is of order \(O_p (n^{-1/d})\). This is for \(d=1,2\) in contrast to the complete distance where worse rates are known. There is a close connection to the combinatorial problem of optimal incomplete matching as well as to the problem of random quantization.