论文标题
多元正常近似的新误差界限通过可交换对以及用于WishArt矩阵的应用和第四次定理的应用
New error bounds in multivariate normal approximations via exchangeable pairs with applications to Wishart matrices and fourth moment theorems
论文作者
论文摘要
我们将斯坦因著名的瓦斯坦（Wasserstein）扩展到了通过可交换对的正常近似限制到多维环境。作为中间步骤，我们利用可交换对的对称性来获得用于平滑测试功能的误差。我们还获得了第四刻的连续版本的多维Wasserstein。我们将主要结果应用于多元正常近似值，以达到$ n $和$ d $的WishArt矩阵，在仅在仅在矩假设的情况下，我们就可以获得最佳的收敛速率$ \ sqrt {n^3/d} $，以及在四分之一时刻的次数和Poisson功能中，我们在四分之一时刻的几点界限中都在文献上占据了范围，在此方面界限了。
We extend Stein's celebrated Wasserstein bound for normal approximation via exchangeable pairs to the multi-dimensional setting. As an intermediate step, we exploit the symmetry of exchangeable pairs to obtain an error bound for smooth test functions. We also obtain a continuous version of the multi-dimensional Wasserstein bound in terms of fourth moments. We apply the main results to multivariate normal approximations to Wishart matrices of size $n$ and degree $d$, where we obtain the optimal convergence rate $\sqrt{n^3/d}$ under only moment assumptions, and to quadratic forms and Poisson functionals, where we strengthen a few of the fourth moment bounds in the literature on the Wasserstein distance.
