论文标题
最大似然估计量的多元正常近似的Wasserstein距离误差界限
Wasserstein distance error bounds for the multivariate normal approximation of the maximum likelihood estimator
论文作者
论文摘要
我们获得了多参数MLE和多元正态分布之间的分布之间的显式$ P $ - WASSERSTEIN距离误差。我们的一般界限是针对高维，独立和相同分布的随机向量的。我们的一般界限是最佳$ \ Mathcal {o}（n^{ - 1/2}）$ order。 Explicit numerical constants are given when $p\in(1,2]$, and in the case $p>2$ the bounds are explicit up to a constant factor that only depends on $p$. We apply our general bounds to derive Wasserstein distance error bounds for the multivariate normal approximation of the MLE in several settings; these being single-parameter exponential families, the normal distribution under canonical parametrisation, and the在非经典参数化下，多变量正态分布。
We obtain explicit $p$-Wasserstein distance error bounds between the distribution of the multi-parameter MLE and the multivariate normal distribution. Our general bounds are given for possibly high-dimensional, independent and identically distributed random vectors. Our general bounds are of the optimal $\mathcal{O}(n^{-1/2})$ order. Explicit numerical constants are given when $p\in(1,2]$, and in the case $p>2$ the bounds are explicit up to a constant factor that only depends on $p$. We apply our general bounds to derive Wasserstein distance error bounds for the multivariate normal approximation of the MLE in several settings; these being single-parameter exponential families, the normal distribution under canonical parametrisation, and the multivariate normal distribution under non-canonical parametrisation. In addition, we provide upper bounds with respect to the bounded Wasserstein distance when the MLE is implicitly defined.
