| Abstract: |
| Stein`s method has been widely used for probability approximations.
However, in the multi-dimensional setting, most of the results are for multivariate normal approximation or for test functions with bounded second or higher order derivatives.
For a class of multivariate limiting distributions, we use Bismut`s formula in Malliavin calculus to control the derivatives of Stein equation solutions by the first derivative of the test function.
Combining with Stein`s exchangeable pair approach, we obtain a general theorem for multivariate approximations with near optimal error bounds on the Wasserstein distance. This is a joint work with Xiao Fang and Qi-Man Shao. |
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