科研之友
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摘要
Let X-1, ... , X-n be i.i.d. random vectors in R-d with parallel to X-1 parallel to <= beta. Then, we show that
1/root n (X-1 + ... + X-n)
converges to a Gaussian in quadratic transportation (also known as "Kantorovich" or "Wasserstein") distance at a rate of O(root d beta log n/root n), improving a result of Valiant and Valiant. The main feature of our theorem is that the rate of convergence is within log n of optimal for n, d -> infinity.
- 出版日期2018-4
